Question: Carco manufactures cars and trucks. Each car contributes $300 to profit, and each truck contributes $400 to profit. The resources required to manufacture a car and truck are shown in the table below:

Each day, Carco can rent up to 98 type 1 machines at a cost of $50 per machine. At present, the company 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. Let

X1 = number of cars produced daily

X2 = number of trucks produced daily

M1 = number of type 1 machines rented daily.

To maximize profit, Carco should solve the following LP:

Max 300X1 +400 X2 -50 M1

s.t. 0.8 X1 + X2 - M1 \(\le \) 0

M1 \(\le \) 98

0.6X1 + 0.7X2 \(\le \) 73

2X1+ 3X2 \(\le \) 260

X1 \(\ge \) 88

X2 \(\ge \) 26

Solve this LP, and use the output to answer the following question:

1. If cars contribute $310 to profit, what would be the new optimal solution to the problem?
2. What is the most that Carco should be willing to pay to rent an additional type 1 machine for 1 day?
3. What is the most that Carco should be willing to pay for an extra ton of steel?
4. If Carco were required to produce at least 86 cars, what would Carco ^' s profit be?

Please enter the answer to part d - what is the change in profit per additional car produced?

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Solution: The downloadable solution consists of 4 pages
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