Thank you so much in advance. I have trouble with these questions.

Exercise 2-13: Solve the following LP problem by using the graphical procedure and by using excel: For all problems use Excel Solver Maximize Profit = 2X+Y Subject to the constraints 3X+6Y=32 7X+Y=20 3X-Y=3 X,Y =0 Exercise 2-16: Solve the following LP problem using the corner point graphical method. At the optimal solution calculate the slack for each constraint: maximize profit 4x +7y subject to the constraints 2X + 3Y 4X + 2Y X X,Y 60 80 24 0 Exercise 2-18: Solve the following LP problem using graphical procedure and by using Excel: Maximize cost = 4X + 7Y Subject to the constraints 3X + 6Y 100 10X + 2Y 160 2Y 40 2X 75 X,Y 0 Exercise 2-24: A small motor manufacturer makes two types of motors, model A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1.5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0.5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling, and 120 hours of assembly time is available. Each model A sold yields a profit of $22. Each model B can be sold for a $15 profit. If all motors that are assembled can be sold, find the best combination of motors to yield the highest profit. Exercise 3-2: A contestant on the hit reality television show Top Bartender was asked to mix a variety of drinks, each consisting of 4 fluid ounces. No other ingredients were permitted. She was given the following quantities of liquor: Liquor Qty. in (ounces) Bourbon 128 Brandy 128 Vodka 128 Dry Vermouth 32 Sweet Vermouth 32 The contestant is considering making the following four drinks: The New Yorker: 25% each of bourbon, brandy, vodka, and sweet vermouth The Garaboldi: 25% each of brandy and dry vermouth; 50% sweet vermouth The Kentuckian: 100% bourbon The Russian: 75% vodka and 25% dry vermouth The contestant's objective is to make the largest number of drinks with the available liquor. What is the combination of drinks to meet her objective? How I do solve this problem using Excel? solver function? Exercise 3-8: A gear manufacturer is planning next week's production run for four types of gears. If necessary, it is possible to outsource any type of gear from another gear company located nearby. The following table and the table at the bottom of this page show next week's demand, revenue per unit, outsource cost per unit, time (in hours) required per unit in each production process, and the availability and cost of these processes. The nearby company can supply a maximum of 300 units of each type of gear next week. What should be the production and/or outsource pan for the next week to maximize profit? Gear Type Gear A Gear B Gear C Gear D Demand 400 500 450 600 Revenue $12.50 $15.60 $17.40 $19.30 Outsource $7.10 $8.10 $8.40 Exercise 3-12: A political candidate is planning his media budget for an upcoming election. He has $90,500 to spend. His political consultants have provided him with the following estimates of additional votes as a result of the advertising effort: For every small sign placed by the roadside, he will gamer 10 additional votes. For every large sign placed by the roadside, he will gamer 30 additional votes. For every thousand bumper stickers placed on cars, he will gamer 10 additional votes. For every hundred personal mailings to registered voters, he will gamer 40 additional votes, and For every radio ad heard daily in the last month before the election, he will gamer 485 additional votes. The costs for each of these advertising devices, along with the practical minimum and maximum that should be planned for each, are shown on the following table. How should the candidate plan to spend his campaign money? Exercise 3-14: An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income? Investment Expected Interest Maximum Allowed $9.00 Lowincome mortgage loans 7.00% 20% Conventional mortgage loans 6.25% 40% Governmentsponsored mortgage loans 8.25% 25% Bond investments 5.75% 12% Stock investments 8.75% 15% Futures trading 9.50% 10% Exercise 2-13: Solve the following LP problem by using the graphical procedure and by using excel:For all problems use Excel Solver Maximize Profit = 2X+Y Subject to the constraints 3X+6Y=32 7X+Y=20 3X-Y=3 X,Y =0 Exercise 2-13 (Attached graph) The table below gives the possible solution of the graphical problem: Thus, there is no feasible solution for the given linear programming problem. The linear programming model using excel can be formulated as shown below: The above given excel can be solved by using the solver as shown below: Thus, by clicking on the solver button as shown above we can bet the solution of the linear programming problem as given below: Thus, there is no feasible solution for which all the constraints could be satisfied. Exercise 2-16: Solve the following LP problem using the corner point graphical method. At the optimal solution calculate the slack for each constraint: maximize profit 4x +7y subject to the constraints 2X + 3Y 60 4X + 2Y 80 X 24 X,Y 0 X=24 2X+3Y=60 Y=602X/3 =602*24/3 Y=4 Therefore, X=24, Y=4 Cost=4X+7Y =4*247*4 9628 = 68 Cost= $ 68 & X=24, Y=4 Exercise 2-18: Solve the following LP problem using graphical procedure and by using Excel: Maximize cost= 4X + 7Y Subject to the constraints 3X + 6Y 100 10X + 2Y 160 X,Y 2Y 40 2X 75 0 Exercise 2-24: A small motor manufacturer makes two types of motors, model A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1.5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0.5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling, and 120 hours of assembly time is available. Each model A sold yields a profit of $22. Each model B can be sold for a $15 profit. If all motors that are assembled can be sold, find the best combination of motors to yield the highest profit Let x units of A be produced & y of product B. Hence, wiring time = 3x + 2y 8%). How should his investment be diversified to make the most interest income? Investment Low-income mortgage loans Conventional mortgage loans Government-sponsoredmortgage loans Bond investments Stock investments Futures trading Answer: Expected Interest 7.00% 6.25% 8.25% 5.75% 8.75% 9.50% Maximum Allowed 20% 40% 25% 12% 15% 10% Write-up: This problem is a linear programming problem with Six decision variables which are the number of six different Investment options. We have to maximize the total Interest Income, Subjected to the constraints. This problem can be formulated in excel and can be solved using the solver module. Decision Variables: X1 = Amount invested in Low-income mortgage loans. X2 = Amountinvested in Conventional mortgage loans. X3 = Amount investedin Governmetn-sposoredmortgage loans. X4 = Amount investedin Bond Investments. X5 = Amount investedin Stock Investments. X6 = Amount investedin Future trading. Constraints: 1 2 3 4 5 6 7 8 9 He wants at least 35% of his investments to be in nonmortgage instruments. X4 + X5 + X6 >= 0.35*12.5 million. He wants no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest >8%). X3 + X5 + X6 = 3 X, Y >= 0 SOLVER SOLUTION Solution Obj coeff Constraints: Constraint 1 Constraint 2 Constraint 3 X 2.30 2 3 7 3 SOLVER SOLUTION Y 3.90 1 6 1 -1 8.50 30.30 = LHS Sign 32 20 3 RHS CONSTRAINT 1 3X + 6Y = 3 3X - Y = 3 -Y = 3 - 3X Y=X-1 X Y 0 2 4 6 8 -1 1 3 5 7 +Y 3X + 6y = 3 20 25 X Y 2.3 C1 C2 C3 3 7 3 Profit 3.9 Constraints 30.3 = 20 = 3= 8.5 6= 1= -1 = 32 20 3 32 20 3 25 C1 X Y 0 5.333333 10.66667 0 20 15 C2 X Y 0 2.857143 C3 X 20 0 Y 0 1 10 5 0 -3 0 Thus there is no feasible solution to this problem. -5 0 2 4 6 8 10 12 8 10 12 X C1 C2 C3 Y Profit 1 2 2 4 1 3= 2= 0= Point A B C 18 60 80 24 X Y 0 15 24 40 10 4 45 A C1 X Y 0 30 20 0 40 35 30 C2 X 25 Y 0 20 40 0 20 15 B 10 C3 X Y 0 24 #DIV/0! 0 Profit is maximized at 0,40 C 5 0 0 5 10 15 20 25 30 35 Profit 280 130 124 25 30 35 X Y 1 C1 C2 C3 C4 3 10 0 2 Cost 2 6= 2= 2= 0= Point A B C 18 100 160 40 75 90 A X Y 0 12 37.5 80 20 20 80 C1 X Y 0 16.66667 33.33333 0 70 60 Feasible region 50 C2 X 40 Y 0 16 80 0 30 20 C3 X Y 0 #DIV/0! C4 X 10 20 0 Y 0 37.5 B #DIV/0! 0 Cost is maximized at X=0 and Y=80 0 0 5 10 15 20 25 30 35 40 Cost 560 188 290 C 30 35 40 Maximize X Y 0 Constraints Wiring time Drilling time Assembly time Profit 120 1800 Actual time 3 2 1.5 2 1 0.5 Maximum time 240 240 120 210 60 120 Decision variables TNY Number of drinks Constraints Maximum Bourbon Maximum Brandy Maximum Vodka Maximum Dry Vermouth Maximum sweet Vermouth TG TK 32 0 1 1 1 1 1 TR 24 32 4 1 2 3 1 Objective function 88 128 = 300 = 40 = 800 = 4 = 90500 500 100 300 50 100 40 800 500 12 3 Decision variable Values Expected interest L C G B S F total 2.5 0.07 2.5 0.0625 3.125 0.0825 1.25 0.0575 1.875 0.0875 1.25 0.095 0.94375 2.5 2.5 3.125 1.25 1.875 1.25 12.5 35% investment in non mortgage 0 0 0 1 1 1 4.375 Maximum 60% in high risk instruments 0 0 1 0 1 1 6.25 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2.5 2.5 3.125 1.25 1.875 1.25 CONSTRAINTS Budget Maximum per instrument = $ 4.38 = 3 X, Y >= 0 SOLVER SOLUTION Solution Obj coeff Constraints: Constraint 1 Constraint 2 Constraint 3 X 2.30 2 3 7 3 SOLVER SOLUTION Y 3.90 1 6 1 -1 8.50 30.30 = LHS Sign 32 20 3 RHS CONSTRAINT 1 3X + 6Y = 3 3X - Y = 3 -Y = 3 - 3X Y=X-1 X Y 0 2 4 6 8 -1 1 3 5 7 +Y 3X + 6y = 3 20 25 X Y 2.3 C1 C2 C3 3 7 3 Profit 3.9 Constraints 30.3 = 20 = 3= 8.5 6= 1= -1 = 32 20 3 32 20 3 25 C1 X Y 0 5.333333 10.66667 0 20 15 C2 X Y 0 2.857143 C3 X 20 0 Y 0 1 10 5 0 -3 0 Thus there is no feasible solution to this problem. -5 0 2 4 6 8 10 12 8 10 12 X C1 C2 C3 Y Profit 1 2 2 4 1 3= 2= 0= Point A B C 18 60 80 24 X Y 0 15 24 40 10 4 45 A C1 X Y 0 30 20 0 40 35 30 C2 X 25 Y 0 20 40 0 20 15 B 10 C3 X Y 0 24 #DIV/0! 0 Profit is maximized at 0,40 C 5 0 0 5 10 15 20 25 30 35 Profit 280 130 124 25 30 35 X Y 1 C1 C2 C3 C4 3 10 0 2 Cost 2 6= 2= 2= 0= Point A B C 18 100 160 40 75 90 A X Y 0 12 37.5 80 20 20 80 C1 X Y 0 16.66667 33.33333 0 70 60 Feasible region 50 C2 X 40 Y 0 16 80 0 30 20 C3 X Y 0 #DIV/0! C4 X 10 20 0 Y 0 37.5 B #DIV/0! 0 Cost is maximized at X=0 and Y=80 0 0 5 10 15 20 25 30 35 40 Cost 560 188 290 C 30 35 40 Maximize X Y 0 Constraints Wiring time Drilling time Assembly time Profit 120 1800 Actual time 3 2 1.5 2 1 0.5 Maximum time 240 240 120 210 60 120 Decision variables TNY Number of drinks Constraints Maximum Bourbon Maximum Brandy Maximum Vodka Maximum Dry Vermouth Maximum sweet Vermouth TG TK 32 0 1 1 1 1 1 TR 24 32 4 1 2 3 1 Objective function 88 128 = 300 = 40 = 800 = 4 = 90500 500 100 300 50 100 40 800 500 12 3 Decision variable Values Expected interest L C G B S F total 2.5 0.07 2.5 0.0625 3.125 0.0825 1.25 0.0575 1.875 0.0875 1.25 0.095 0.94375 2.5 2.5 3.125 1.25 1.875 1.25 12.5 35% investment in non mortgage 0 0 0 1 1 1 4.375 Maximum 60% in high risk instruments 0 0 1 0 1 1 6.25 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2.5 2.5 3.125 1.25 1.875 1.25 CONSTRAINTS Budget Maximum per instrument = $ 4.38