Question

18. An automotive plant makes the Quartz and the Pacer. The plant has a maximum production capacity of 1200 cars per week, and they can make at most 600 Quartz cars and 800 Pacers each week. If the profit on a Quartz is $500 and the profit on a Pacer is $800, find how many of each type of car the plant should produce. Quartz PacersWhat is the maximum profit? $

Answer 1

First,

Let x be the Quartz and let y be the Pacer.

We can write:

x+y≤1200 ( maximum production capacity of 1200 cars per week)

We also know that:

0≤x≤600

0≤y≤800

And, the profit is given by the expression: 500x+800y

At a point, we got that : x=0 and y=800. So, if we replace this:

Profit=500x+800y ⇒ 500(0) + 800(800)= 640000

When x=600(max), y=0:

profit = 500(600) + 0 = 300000

Using (x,y) = (600,600):

Profit = 500(600)+800(600)= 780000

And, if we make x=400 and y=800:

Profit =500(400)+800(800) = 840000. This is the maximum profit, and it occurs when Quartz = 400 and Pacers = 800.