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Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400; these profits do not consider machine rental. The resources required to manufacture a car and a truck are shown below. Each day Carco can rent up to 98 Type 1 machines at a cost of $50 per machine. The company now has 73 Type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Part A: Formulate the problem as a Linear Program. Part B: Solve the LP (provide exact values for all variables and the optimal objective function). Hint: The optimal objective function value is $32540 [Note, I am providing this hint because having the optimal solution is necessary to do Part C.] Part C: Answer the following questions from your output. (Note, do not simply rerun the model – use the Linear Programming output and Sensitivity Analysis to explain your answers.) iv) If Carco were required to produce at least 86 cars, what would Carco's profit become? v) Carco is considering producing jeeps. A jeep contributes $600 to profit and requires 1.2 days on machine 1, 2 days on machine 2, and 4 tons of steel. Should Carco produce any jeeps? Table: Days on Machine 2 0.6 Vehicle Type Days on Machine 1 Tons of Steel Car 0.8 2 Truck 1 0.7 3

Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400; these profits do not consider machine rental. The resources required to manufacture a car and a truck are shown below. Each day Carco can rent up to 98 Type 1 machines at a cost of $50 per machine. The company now has 73 Type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Part A: Formulate the problem as a Linear Program. Part B: Solve the LP (provide exact values for all variables and the optimal objective function). Hint: The optimal objective function value is $32540 [Note, I am providing this hint because having the optimal solution is necessary to do Part C.] Part C: Answer the following questions from your output. (Note, do not simply rerun the model – use the Linear Programming output and Sensitivity Analysis to explain your answers.) iv) If Carco were required to produce at least 86 cars, what would Carco's profit become? v) Carco is considering producing jeeps. A jeep contributes $600 to profit and requires 1.2 days on machine 1, 2 days on machine 2, and 4 tons of steel. Should Carco produce any jeeps? Table: Days on Machine 2 0.6 Vehicle Type Days on Machine 1 Tons of Steel Car 0.8 2 Truck 1 0.7 3

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 115P
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Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400; these profits do not consider machine rental. The resources required to manufacture a car and a truck are shown below. Each day Carco can rent up to 98 Type 1 machines at a cost of $50 per machine. The company now has 73 Type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Part A: Formulate the problem as a Linear Program. Part B: Solve the LP (provide exact values for all variables and the optimal objective function). Hint: The optimal objective function value is $32540 [Note, I am providing this hint because having the optimal solution is necessary to do Part C.] Part C: Answer the following questions from your output. (Note, do not simply rerun the model – use the Linear Programming output and Sensitivity Analysis to explain your answers.) iv) If Carco were required to produce at least 86 cars, what would Carco's profit become? v) Carco is considering producing jeeps. A jeep contributes $600 to profit and requires 1.2 days on machine 1, 2 days on machine 2, and 4 tons of steel. Should Carco produce any jeeps? Table: Vehicle Type Days on Machine 1 Days on Machine 2 Tons of Steel Car 0.8 0.6 2 Truck 1 0.7 3
Transcribed Image Text:Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400; these profits do not consider machine rental. The resources required to manufacture a car and a truck are shown below. Each day Carco can rent up to 98 Type 1 machines at a cost of $50 per machine. The company now has 73 Type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Part A: Formulate the problem as a Linear Program. Part B: Solve the LP (provide exact values for all variables and the optimal objective function). Hint: The optimal objective function value is $32540 [Note, I am providing this hint because having the optimal solution is necessary to do Part C.] Part C: Answer the following questions from your output. (Note, do not simply rerun the model – use the Linear Programming output and Sensitivity Analysis to explain your answers.) iv) If Carco were required to produce at least 86 cars, what would Carco's profit become? v) Carco is considering producing jeeps. A jeep contributes $600 to profit and requires 1.2 days on machine 1, 2 days on machine 2, and 4 tons of steel. Should Carco produce any jeeps? Table: Vehicle Type Days on Machine 1 Days on Machine 2 Tons of Steel Car 0.8 0.6 2 Truck 1 0.7 3
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