Question: Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400. 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 cars produce daily

X2 - number of trucks produced daily

M1 - type 1 machines rented daily

To maximize profit, Carco should solve the following LP (it's okay to get fractional solutions - this is only for planning purposes).

\(\operatorname{Max} 300 \times 1+400 \times 2-50 \mathrm{M} 1\)

Subject to:

\(0.6 \times 1+0.7 \times 2<=73\)

\(2 \times 1+3 \times 2<=260\)

\(\mathrm{X} 1>=88\)

\(\mathrm{X} 2>=26\)

\(\mathrm{X} 1>=0 ; \mathrm{X} 2>=0\)

1. Formulate the dual problem.
2. Solve the problem using MPL.
   Use the MPL output to answer the questions below.
3. If cars contributed $310 to profit, what would be the new optimal solution to the problem?
4. What is the most that Carco should be willing to pay to rent an additional type 1 machine for 1 day?
5. What is the most that Carco should be willing to pay for an extra ton of steel?
6. If Carco was required to produce at least 86 cars, what would Carco's profit become?
7. 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 jeep?

Price: $2.99

Solution: The downloadable solution consists of 5 pages
Deliverable: Word Document