Question

I need help with this question, check the 1st part and answer the 2nd part please.

Answer 1

Given the function of the profit P(x)

`P(x)=150x-x^2`

Part (b):

We will find the number of cases of pies to maximize the profit.

the given function has a negative leading coefficient and from part (a) the function will be zero when x = 0 and x = 150

Form the symmetry of the quadratic function, the maximum point will be in the middle between x = 0, and x = 150

so, the middle point will be as follows:

`x=(0+150)/(2)=75`

So, the maximum profit will be at x = 75

Substitute x = 75 into P(x)

`P(75)=150*75-75^2=5625`

So, the answer will be:

The number of cases of pies to maximize the profit = 75

The maximum profit = $5625