1. Consider the sensitivity report below for problems 1-5. The optimal solution to this linear program is x1 = 34, x2 = 40. x1 = 6, x2 = 11. x1 = 3, x2 = 6. x1 = 0, x2 = 0. x1 = 7.33, x2 = 6. 2. Which of the following constraints are binding? Packing only Additive only Extrusion and Packaging Extrusion only All constraints are binding 3. What is the increase in the objective value if 2 units of extrusion are added? 3 Not enough information provided 96 6 48 4. What is the increase in the objective value if 2 units of packaging are added? 18 36 11 22 Not enough information provided 5. What is the increase in the objective value if 2 units of additive is added? 4 12 16 Not enough information provided 0 Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure. Their weekly advertising budget is $10,000. They are considering three possible media: tv, newspaper, and radio. Information regarding cost and exposure is given in the table below: Medium TV Newspaper Radio audience reached per ad 7,000 8,500 3,000 maximum cost per ads per ad ($) week 800 10 1000 7 400 20 Use the above information to solve questions 6-9 6. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What would the objective function be? Minimize 7000T + 8500N + 3000R Maximize 7000T + 8500N + 3000R Minimize 10T + 7N + 20R Minimize 800T + 1000N + 400R 7. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What is the advertising budget constraint? 800T + 1000N + 400R 10,000 800T + 1000N + 400R 10,000 10T + 7N + 20R 10,000 10T + 7N + 20R 10,000 7000T + 8500N + 3000R 10,000 8. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads Which of the following set of inequalities properly represent the limits on advertisements per week by media? T + R + N 37 10N + 7N + 20T 10,000 T + R + N 37 T 10; N 7; R 20 T 10; N 7; R 20 9. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What is the optimal solution? T = 10; N = 0; R = 0 T = 10; N = 2; R = 0 T = 10; N = 7; R = 20 Solution is unbounded Solution is infeasible A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below: The requirements for the survey are as follows: The survey must have at least 1500 students. At least 400 graduate students. At least 100 graduate students should be from the West. No more than 500 undergraduate students should be from the East. At least 75 graduate students should be from the Central region and finally, At least 300 students should be from the West. Use the above information to solve questions 10 - 13 10. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. What is the objective function? Maximize 10X1 + 12X2 + 15X3 + 15X4 + 18X5 + 21X6 Minimize 10X1 + 12X2 + 15X3 + 15X4 + 18X5 + 21X6 Minimize 1500X1 + 400X2 + 100X3 + 500X4 + 75X5 + 300X6 Maximize 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 Minimize 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 M i n i m i z e 1 0 X 1 + 1 5 X 2 + 1 2 X 3 + 1 8 X 4 + 1 5 X 5 + 2 1 X 6 11. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The constraint that the survey must have at least a total of 1500 students is expressed as 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 1500. X1 + X2 + X3 + X4 + X5 + X6 1500. X1 + X3 + X5 1500. 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 1500. X1 + X2 + X3 + X4 + X5 + X6 1500. 12. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The constraint that there must be at least 400 graduate students is expressed as X1 + X2 + X3 + X4 + X5 + X6 400. X1 + X2 + X3 400. X2 + X4 + X6 400. X1 + X3 + X5 400. X1 + X2 + X3 + X4 + X5 + X6 400. 13. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The minimum survey cost is 19625 20500 18950 19400 20000 The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X 1 - X4 represent the number of employees assigned to each shift, i.e., starting work on each shift (shift 1 through shift 4). Use the above information to answer questions 14 - 21 14. How many workers would be assigned to shift 1? 0 12 None of the alternatives are correct. 13 2 15. How many workers would be assigned to shift 3? None of the alternatives are correct 0 13 16 14 16. How many workers would be assigned to shift 2? 14 0 None of the alternatives are correct 2 15 17. How many workers would be assigned to shift 4? 16 1 None of the alternatives are correct 14 0 18. How many workers would actually be on duty during shift 1? 29 13 12 0 None of the alternatives are correct 19. How many workers would actually be on duty during shift 4? 15 12 16 14 None of the alternatives are correct 20. Which shift would have more workers than needed? Shift 1 Shift 3 Shift 2 None of the alternatives are correct Shift 4 21. Which shift would have fewer workers than needed? Shift 4 Shift 2 Shift 3 Shift 1 None of the alternatives are correct Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows: C = dollars invested in CDs S = dollars invested in stocks M = dollars invested in the money market mutual fund Use the above information to answer questions 22-23 22. Which of the following would be the most appropriate constraint in the linear programming problem? C + S + M 200000 C + S + M = 200000 0.06C + 0.13S + 0.08M 200000 None of the alternatives are correct C + S + M 200000 23. Suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested. Which is the best way to write this constraint? S (C + M) / 4 -C + 3S - M 0 0.13S 0.24C + 0.32M -C + 4S - M 0 S 100,000/4 Capital Budgeting Inc has to select among six possible projects without exceeding its total investment budget of $10,000. It's objective is to maximize the NPV (Net Present Value) of all future earnings form the projects it selects to invest in. The information on the six possible projects for investment is as follows: Project Net Present Value (NPV) Of Future Earnings Investment Required 1 $22,500 $7,500 2 $24,000 $7,500 3 $8,000 $3,000 4 $9,500 $3,500 5 $11,500 $4,000 6 $9,750 $3,500 Use the information above to answer questions 24 - 27 24. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the optimal investment would be: $1500 in Project 3 and $2,500 in Project 2 $2500 in Project 1 and $7,500 in Project 2 $2000 in Project 6 and $7,500 in Project 2 $2000 in Project 1 and $7,500 in Project 2 $2500 in Project 1 and $7,500 in Project 2 25. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the max NPV it can earn when it selects its projects optimally is equal to None of the alternatives are correct. $27,250 $31, 500 $35,000 $27,550 26. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, it can be assumed that at optimality, Capital Budgeting Inc would have invested its entire budget. True False 27. Assuming that Capital Budgeting Inc is not allowed to invest partially in any of the projects (i.e., it has to either fully invest in a project or not at all) the optimal investment would be: $1500 in Project 3 and $2,500 in Project 2 $3,000 in Project 3, $3,500 in Project 4 and $3,500 in Project 6 $2000 in Project 1, $1,500 in Project 1 and $6,500 in Project 4 $3,000 in Project 1, $5,500 in Project 2 and $1,500 in Project 6 $2,500 in Project 1, $4,500 in Project 2 and $3,000 in Project 5 1. Consider the sensitivity report below for problems 1-5. The optimal solution to this linear program is x1 = 34, x2 = 40. x1 = 6, x2 = 11. x1 = 3, x2 = 6. x1 = 0, x2 = 0. x1 = 7.33, x2 = 6. 2. Which of the following constraints are binding? Packing only Additive only Extrusion and Packaging Extrusion only All constraints are binding 3. What is the increase in the objective value if 2 units of extrusion are added? 3 Not enough information provided 96 6 48 4. What is the increase in the objective value if 2 units of packaging are added? 18 36 11 22 Not enough information provided 5. What is the increase in the objective value if 2 units of additive is added? 4 12 16 Not enough information provided 0 Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure. Their weekly advertising budget is $10,000. They are considering three possible media: tv, newspaper, and radio. Information regarding cost and exposure is given in the table below: Medium TV Newspaper Radio audience reached per ad 7,000 8,500 3,000 maximum cost per ads per ad ($) week 800 10 1000 7 400 20 Use the above information to solve questions 6-9 6. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What would the objective function be? Minimize 7000T + 8500N + 3000R Maximize 7000T + 8500N + 3000R Minimize 10T + 7N + 20R Minimize 800T + 1000N + 400R 7. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What is the advertising budget constraint? 800T + 1000N + 400R 10,000 800T + 1000N + 400R 10,000 10T + 7N + 20R 10,000 10T + 7N + 20R 10,000 7000T + 8500N + 3000R 10,000 8. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads Which of the following set of inequalities properly represent the limits on advertisements per week by media? T + R + N 37 10N + 7N + 20T 10,000 T + R + N 37 T 10; N 7; R 20 T 10; N 7; R 20 9. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What is the optimal solution? T = 10; N = 0; R = 0 T = 10; N = 2; R = 0 T = 10; N = 7; R = 20 Solution is unbounded Solution is infeasible A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below: The requirements for the survey are as follows: The survey must have at least 1500 students. At least 400 graduate students. At least 100 graduate students should be from the West. No more than 500 undergraduate students should be from the East. At least 75 graduate students should be from the Central region and finally, At least 300 students should be from the West. Use the above information to solve questions 10 - 13 10. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. What is the objective function? Maximize 10X1 + 12X2 + 15X3 + 15X4 + 18X5 + 21X6 Minimize 10X1 + 12X2 + 15X3 + 15X4 + 18X5 + 21X6 Minimize 1500X1 + 400X2 + 100X3 + 500X4 + 75X5 + 300X6 Maximize 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 Minimize 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 M i n i m i z e 1 0 X 1 + 1 5 X 2 + 1 2 X 3 + 1 8 X 4 + 1 5 X 5 + 2 1 X 6 11. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The constraint that the survey must have at least a total of 1500 students is expressed as 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 1500. X1 + X2 + X3 + X4 + X5 + X6 1500. X1 + X3 + X5 1500. 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 1500. X1 + X2 + X3 + X4 + X5 + X6 1500. 12. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The constraint that there must be at least 400 graduate students is expressed as X1 + X2 + X3 + X4 + X5 + X6 400. X1 + X2 + X3 400. X2 + X4 + X6 400. X1 + X3 + X5 400. X1 + X2 + X3 + X4 + X5 + X6 400. 13. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The minimum survey cost is 19625 20500 18950 19400 20000 The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X 1 - X4 represent the number of employees assigned to each shift, i.e., starting work on each shift (shift 1 through shift 4). Use the above information to answer questions 14 - 21 14. How many workers would be assigned to shift 1? 0 12 None of the alternatives are correct. 13 2 15. How many workers would be assigned to shift 3? None of the alternatives are correct 0 13 16 14 16. How many workers would be assigned to shift 2? 14 0 None of the alternatives are correct 2 15 17. How many workers would be assigned to shift 4? 16 1 None of the alternatives are correct 14 0 18. How many workers would actually be on duty during shift 1? 29 13 12 0 None of the alternatives are correct 19. How many workers would actually be on duty during shift 4? 15 12 16 14 None of the alternatives are correct 20. Which shift would have more workers than needed? Shift 1 Shift 3 Shift 2 None of the alternatives are correct Shift 4 21. Which shift would have fewer workers than needed? Shift 4 Shift 2 Shift 3 Shift 1 None of the alternatives are correct Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows: C = dollars invested in CDs S = dollars invested in stocks M = dollars invested in the money market mutual fund Use the above information to answer questions 22-23 22. Which of the following would be the most appropriate constraint in the linear programming problem? C + S + M 200000 C + S + M = 200000 0.06C + 0.13S + 0.08M 200000 None of the alternatives are correct C + S + M 200000 23. Suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested. Which is the best way to write this constraint? S (C + M) / 4 -C + 3S - M 0 0.13S 0.24C + 0.32M -C + 4S - M 0 S 100,000/4 Capital Budgeting Inc has to select among six possible projects without exceeding its total investment budget of $10,000. It's objective is to maximize the NPV (Net Present Value) of all future earnings form the projects it selects to invest in. The information on the six possible projects for investment is as follows: Project Net Present Value (NPV) Of Future Earnings Investment Required 1 $22,500 $7,500 2 $24,000 $7,500 3 $8,000 $3,000 4 $9,500 $3,500 5 $11,500 $4,000 6 $9,750 $3,500 Use the information above to answer questions 24 - 27 24. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the optimal investment would be: $1500 in Project 3 and $2,500 in Project 2 $2500 in Project 1 and $7,500 in Project 2 $2000 in Project 6 and $7,500 in Project 2 $2000 in Project 1 and $7,500 in Project 2 $2500 in Project 1 and $7,500 in Project 2 25. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the max NPV it can earn when it selects its projects optimally is equal to None of the alternatives are correct. $27,250 $31, 500 $35,000 $27,550 26. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, it can be assumed that at optimality, Capital Budgeting Inc would have invested its entire budget. True False 27. Assuming that Capital Budgeting Inc is not allowed to invest partially in any of the projects (i.e., it has to either fully invest in a project or not at all) the optimal investment would be: $1500 in Project 3 and $2,500 in Project 2 $3,000 in Project 3, $3,500 in Project 4 and $3,500 in Project 6 $2000 in Project 1, $1,500 in Project 1 and $6,500 in Project 4 $3,000 in Project 1, $5,500 in Project 2 and $1,500 in Project 6 $2,500 in Project 1, $4,500 in Project 2 and $3,000 in Project 5 Consider the sensitivity report below for problems 1-4. 1. Which of the following constraints are binding? Packing only Additive only Extrusion and Packaging Extrusion only All constraints are binding 2. What is the increase in the objective value if 2 units of extrusion are added? 3 Not enough information provided 96 6 48 3. What is the increase in the objective value if 2 units of packaging are added? 18 36 11 22 Not enough information provided 4. What is the increase in the objective value if 2 units of additive is added? 4 12 16 Not enough information provided 0 Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure. Their weekly advertising budget is $10,000. They are considering three possible media: tv, newspaper, and radio. Information regarding cost and exposure is given in the table below: Medium TV Newspaper Radio audience reached per ad 7,000 8,500 3,000 maximum cost per ads per ad ($) week 800 10 1000 7 400 20 Use the above information to solve questions 5-7 5. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What is the advertising budget constraint? 800T + 1000N + 400R 10,000 800T + 1000N + 400R 10,000 10T + 7N + 20R 10,000 10T + 7N + 20R 10,000 7000T + 8500N + 3000R 10,000 6. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads Which of the following set of inequalities properly represent the limits on advertisements per week by media? T + R + N 37 10N + 7N + 20T 10,000 T + R + N 37 T 10; N 7; R 20 T 10; N 7; R 20 7. Let T = the # of tv ads, N = the # of newspaper ads, and R = the # of radio ads What is the optimal solution? T = 10; N = 0; R = 0 T = 10; N = 2; R = 0 T = 10; N = 7; R = 20 Solution is unbounded Solution is infeasible A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below: The requirements for the survey are as follows: The survey must have at least 1500 students. At least 400 graduate students. At least 100 graduate students should be from the West. No more than 500 undergraduate students should be from the East. At least 75 graduate students should be from the Central region and finally, At least 300 students should be from the West. Use the above information to solve questions 8 - 11 8. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. What is the objective function? Maximize 10X1 + 12X2 + 15X3 + 15X4 + 18X5 + 21X6 Minimize 10X1 + 12X2 + 15X3 + 15X4 + 18X5 + 21X6 Minimize 1500X1 + 400X2 + 100X3 + 500X4 + 75X5 + 300X6 Maximize 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 Minimize 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 M i n i m i z e 1 0 X 1 + 1 5 X 2 + 1 2 X 3 + 1 8 X 4 + 1 5 X 5 + 2 1 X 6 9. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The constraint that the survey must have at least a total of 1500 students is expressed as 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 1500. X1 + X2 + X3 + X4 + X5 + X6 1500. X1 + X3 + X5 1500. 10X1 + 15X2 + 12X3 + 18X4 + 15X5 + 21X6 1500. X1 + X2 + X3 + X4 + X5 + X6 1500. 10. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The constraint that there must be at least 400 graduate students is expressed as X1 + X2 + X3 + X4 + X5 + X6 400. X1 + X2 + X3 400. X2 + X4 + X6 400. X1 + X3 + X5 400. X1 + X2 + X3 + X4 + X5 + X6 400. 11. The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X 4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region. The minimum survey cost is 19625 18950 19400 20000 The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X 1 - X4 represent the number of employees assigned to each shift, i.e., starting work on each shift (shift 1 through shift 4). Use the above information to answer questions 12 - 12. How many workers would be assigned to shift 1? 0 12 None of the alternatives are correct. 13 2 13. How many workers would be assigned to shift 3? None of the alternatives are correct 0 13 16 14 14. How many workers would be assigned to shift 2? 14 0 None of the alternatives are correct 2 15 15. How many workers would be assigned to shift 4? 16 1 None of the alternatives are correct 14 0 16. How many workers would actually be on duty during shift 1? 29 13 12 0 None of the alternatives are correct 17. How many workers would actually be on duty during shift 4? 15 12 16 14 None of the alternatives are correct 18. Which shift would have more workers than needed? Shift 1 Shift 3 Shift 2 None of the alternatives are correct Shift 4 19. Which shift would have fewer workers than needed? Shift 4 Shift 2 Shift 3 Shift 1 None of the alternatives are correct Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows: C = dollars invested in CDs S = dollars invested in stocks M = dollars invested in the money market mutual fund 20. Suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested. Which is the best way to write this constraint? S (C + M) / 4 -C + 3S - M 0 0.13S 0.24C + 0.32M -C + 4S - M 0 S 100,000/4 Capital Budgeting Inc has to select among six possible projects without exceeding its total investment budget of $10,000. It's objective is to maximize the NPV (Net Present Value) of all future earnings form the projects it selects to invest in. The information on the six possible projects for investment is as follows: Project Net Present Value (NPV) Of Future Earnings Investment Required 1 $22,500 $7,500 2 $24,000 $7,500 3 $8,000 $3,000 4 $9,500 $3,500 5 $11,500 $4,000 6 $9,750 $3,500 Use the information above to answer questions 24 - 27 21. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the optimal investment would be: $1500 in Project 3 and $2,500 in Project 2 $2500 in Project 1 and $7,500 in Project 2 $2000 in Project 6 and $7,500 in Project 2 $2000 in Project 1 and $7,500 in Project 2 $2500 in Project 1 and $7,500 in Project 2 22. Assuming that Capital Budgeting Inc is allowed to invest partially in any of the projects with expectation that the NPV will be reduced proportionally, the max NPV it can earn when it selects its projects optimally is equal to None of the alternatives are correct. $27,250 $31, 500 $35,000 $27,550 A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows: T = number of tables produced each week C = number of chairs produced each week Suppose it is decided that there must be 4 chairs produced for every table. How would this constraint be written? TC 4T = C T = 4C TC Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond. The company wishes to reach as many respondents as possible while meeting all the constraints stated. If this is formulated as a LP model, with R = number of radio ads placed and N = number of newspaper ads placed, the objective function would be: Min 200R + 300N Max 40R + 300N Max 400R + 3000N Max 4000R + 3000N Max 2000R + 3000N