Tom Peterson is starting a car rental company and has a budget of $2,000,000. He

Question

Tom Peterson is starting a car rental company and has a budget of $2,000,000. He plans to buy automobiles, SUVs, and trucks to satisfy client's demands. The esti- mated costs are as follows: Price of an automobile: $35,000 Price of a SUV: $40,000 Price of a truck: $60,000 He expects to earn $2,000 profit from an automobile, $4,500 from an SUV and $3850 from a truck per month. He wants to buy at least two vehicles of each type. In addition, because the demand of automobiles is much higher than SUVs and trucks, automobiles should comprise at least 2/3 of his fleet. Formulate a linear program model to help Tom maximize his monthly profit. (Define decision variables and write the objective function and constraints.)

Explanation / Answer

decision variables
x = automobile ,
y = SUV
z= truck

objective function
maximize
Z = 2000x + 4500y + 3850z

constraints
x>= 2 ,
y>= 2 ,
z>= 2
35000x + 40000y +60000 <= 2000000
x >= 2/3 (x+y+z)     (ignore this if you want)

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