Acompany finds that it can make a profit of p dollars each month by selling x patterns, according to the formula p ( x ) = − .002 x 2 + 5.5 x − 600 . how many patterns must it sell each month to have a maximum profit? to attain maximum profit they must sell patterns. what is the maximum profit? the max profit is $ .

It must sell 1,375 patterns each month in order to attain maximum profit, and that maximum profit is $3,181.25

Explanation:

In order to find the number of patterns that will translate into the maximum profit for the compamy, first we have to consider that the equation given is actually a parabola, and its vertex, when we draw it (Y equals profit and X equals units) proposes the maximum profit possible (if the formula continues to describe the company´s profit).

With that in mind, the general equation of a parabola is as follows.

in our case

a= - 0.002

b= 5.5

c= -600

And the formula, to find the quantity that will provide the maximum profit (x coordinate of the parabola) is as follows.

Therefore

Now, if we want to find what is going to be this maximum profit in terms of dollars, we just have to substitute x for 1,375 in the equation given, that is.

Best of luck.

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