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

Each day, Carco can rent up to 98 Type 1 machines at 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. Carco aims to maximize profit. The LP formulation and its solution in LINGO are given below.

(a) If cars contributed $310 to profit, what would be the new optimal profit? Just enter an integer number (no dollar signs, commas, or dots).

(b) Consider the following question:

What is the most that Carco should be willing to pay to rent an additional Type 1 machine for 1 day?

Note that since the allowable increase for type 1 machines is less than one, we cannot answer this question.

Now assume Carco could rent an additional Type 1 machine for 1/5 of a day.

What is the most that Carco should be willing to pay for such a rent? Just enter an integer number (no dollar signs, commas, or dots)

(c) What is the most that Carco should be willing to pay for an extra ton of steel? Just enter an integer number (no dollar signs, commas, or dots)

(d) If Carco were required to produce at least 86 cars, what would Carco's profit become? Just enter an integer number (no dollar signs, commas, or dots)

(e) Carco is considering producing jeeps. A jeep contributes $530 to profit and requires 1.2 days on machine 1, 2 days on machine 2, and 4 tons of steel. Price out the new variable x₃ representing the number of jeeps (that is, compute c₃-c_B^TB^-1a₃). What do you obtain?

Should Carco produce any jeeps?