An auto company manufactures cars, pickup trucks, and sport utility vehicles (SUV's).
The parts for the body of each vehicle must be stamped out on a press, undercoated, then
¯nish-painted. Suppose the press line can press 35 car bodies per day if just cars are being
made (that is, it requires 1/35 of a day to press one car body), 28 truck bodies per day if
just trucks are being made, and 24.5 SUV bodies per day if just SUV's are being made. The
undercoating line could coat 40 car bodies per day if just cars were being made, 30 trucks
per day if just trucks were being made, and 24 SUV's per day if just SUV's were being made.
The paint line could paint 30 car bodies per day if just cars were being made, 40 trucks per
day if just trucks were being made, and 40 SUV's per day if just SUV's were being made.
Assume that the rate at which the vehicles are stamped and painted does not change if a
combination of vehicles are made during the day. The pro¯t on a car, truck and SUV are
$3500, $4500, $5500 respectively.
(a) Set up the linear program that will maximize profits.
(b) Clearly explain why the simplex algorithm can be used to attempt to solve this linear
program and form the initial simplex table.
(c) Solve the linear program.
(d) In the context of the word problem, clearly explain the meaning of the slack variables
de¯ned by the basic feasible solution of the final simplex table.
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