A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company’s profit. (Hint: One approach, but not the only approach, is to try a graphical procedure first and then deduce the constraints from the graph.)

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MrRoyal MrRoyal · Answer 1 · 2022-02-21T15:42:52+01:00

The trucks manufactured by the company are illustrations of linear programming

The optimal solution is (0,700)

Represent truck 1 with x and truck 2 with y.

The profit from each type 1 truck is $1000 while the profit from each type 2 truck is $1500

This means that, the objective function is:

z = 1000x + 1500y

At the painting shop, we have the following inequality

x/800 + y/700 [tex]\le[/tex] 1

At the assembly shop, we have the following inequality,

x/1500 + y/1200 [tex]\le[/tex] 1

So, the linear problem is:

Max z = 1000x + 1500y

Subject to

x/800 + y/700 [tex]\le[/tex] 1

x/1500 + y/1200 [tex]\le[/tex] 1

x, y [tex]\ge[/tex] 0

Next, plot the graphs of the constraints

From the graph, we have the following points:

(x,y) = (0,700), (800,0) and (-6666.7,6533.3)

x and y must be at least 0.

So, we have:

(x,y) = (0,700) and (800,0)

Substitute these values in the objective function

z = 1000 *0 + 1500 *700 = 1050000

z = 1000 *800 + 1500 *0 = 800000

1050000 is greater than 800000.

Hence, the optimal solution is (0,700)

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