Question 1 1 pts Scenario D.1 A local company manufactures two types of ofce desks called type A and B. Each desk requires wood and nails as the main raw materials. The company has 30,000 pounds of wood and 2,500 pounds of nails available. Each Type A desk requires 50 pounds of wood and 3 pounds of nails. The prot generated from each Type A desk is $100. Each Type B desk requires 60 pounds of wood and 4 pounds of nails, and each Type B desk generates a prot of $150. Also current licensing contract limits the manufacturer to make a maximum of 350 units of Type B desks. Referring to Scenario D.1, assume that each pound of wood costs $10 and each pound of nails cost $4. Which of the following statements is correct? 0 The material cost to make one Type B desk is $572. 0 The material cost to make one Type A desk is $512. 0 The material costs to make two Type B desks are $1024. 0 The material costs to make one Type A and one Type B desk are $1224 Question 2 1 pts What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b, subject to (1) 4a + 2b s 16 and (2) 5a + 2b s 20 and (3) a, b 2 0. O a = 0, b = 6 O a = 0, b = 0 O a = 6, b = 0 O a = 3, b = 3 O a = 0, b = 8Question 3 1 pts Riker Co. is considering which of 4 different projects to undertake in order to maximize its net present value (NPV). Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4. The NPV and required capital (in millions) for each project are listed below. Net Present Project Capital Required Value 60 7 2 50 10 3 40 6 4 20 3 What is the proper objective function? O Max 7X1 + 10X2 + 6X3 + 3X4 O Max X1 + X2+ X3 + X4 O Min 60X1 + 50X2 + 40X3 + 20X4 ( Max 170(X1 + X2 + X3 + X4) O Max 60X1 + 50X2 + 40X3 + 20X4Question 4 1 pts Riker Co. is considering which of 4 different projects to undertake in order to maximize its net present value (NPV). Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4. The NPV and required capital (in millions) for each project are listed below. Net Present Project Capital Required Value 60 7 2 50 10 3 40 6 4 20 3 Which of the following represents the constraint(s) stating that project 1 must be undertaken and at least one of the other projects must be undertaken? O X1 + X2 2 1, and X1 + X3 2 1, and X1 + X4 2 1 O X1 + X2 = 1, and X1 + X3 = 1, and X1 + X4 5 1 O X1 +X2 + X3 + X4 22 O X1 2 1, and X2 + X3 + X4 5 3 O X1 21, and X2 + X3 + X4 2 1Question 5 1 pts What combination of x and y will yield the optimum for this problem? Minimize $5x + $20y, subject to (1) x + by s 20 and (2) 2x + By s 16 and (3) x, y 2 0. Ox=0,y=3 Ox=0,y=0 Ox=8,y=0 Ox=1,y=5 Ox=0,y=5 Question 6 Scenario D.1 A local company manufactures two types of ofce desks called type A and B. Each desk requires wood and nails as the main raw materials. The company has 30,000 pounds of wood and 2,500 pounds of nails available. Each Type A desk requires 50 pounds of wood and 3 pounds of nails. The prot generated from each Type A desk is $100. Each Type B desk requires 60 pounds of wood and 4 pounds of nails, and each Type B desk generates a prot of $150. Also current licensing contract limits the manufacturer to make a maximum of 350 units of Type B desks. Referring to Scenario D.1, which of the following statements is correct? 0 Desk A uses more resources and generates a higher prot. 0 Desk A uses less resources but generates a lower prot. 0 Desk B uses more resources but generates a lower prot. 0 Desk B uses less resources and generates a higher prot. 1 pts Question 7 1 pts Download the file ProdMix.xIs from Canvas (Look for the Week 2 Materials in "Modules.") Solve this problem optimally using Excel. Remark: Do not restrict the number of units to be an integer! For this exercise, it is OK to consider the production of fractions of units (e.g., it is fine if the optimal solution shows that you should produce 34.65 tables). If you set your optimization correctly, you will find that the optimal solution for this problem yields an optimal profit of about $101,773. Make sure that you get this value; otherwise, you are likely to mess up the solutions to the following question. What would be the optimal profit if demand was unlimited? In other words, what would be the optimal profit if you could sell any quantities that you can produce? O Infinity O The optimal profit won't change (stay at $101,773). O Less than $101,773. O The optimal profit will increase by about 1%-2%. O The optimal profit will increase by about 2%-5%.Question 8 1 pts Download the le ProdMix.xls from Canvas (Look for the Week 2 Materials in "Modules.") Solve this problem optimally using Excel. Remark: Do not restrict the number of units to be an integer! For this exercise, it is OK to consider the production of fractions of units (e.g., it is ne if the optimal solution shows that you should produce 34.65 tables). If you set your optimization correctly, you will nd that the optimal solution for this problem yields an optimal prot of about $101,773. Make sure that you get this value; otherwise, you are likely to mess up the solutions to the following question. Suppose that you needed to satisfy at least half of the demand for chairs (namely, produce at least 200 chairs). What would be the impact of that constraint on the optimal prot? 0 The optimal prot will decline somewhere between 1% to 5%. O The optimal prot will decline by more than 5%. O The optimal prot will increase by more than 2%. O The optimal prot will remain unchanged. Question 9 1 pts A restaurant manager tracks complaints from the diner satisfaction cards that are turned in at each table. The data collected from the past week's diners have been plotted and appear in the following graph. The number of complaints for each category is with each bar. How was the value for the point represented by the triangle calculated? 0; 55+32+16+13+4+2 O 55+32 55+32 O 55+32 55+32+16+13+4+2