Given the function of the profit P(x)
[tex]P(x)=150x-x^2[/tex]
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:
[tex]x=\frac{0+150}{2}=75[/tex]
So, the maximum profit will be at x = 75
Substitute x = 75 into P(x)
[tex]P(75)=150*75-75^2=5625[/tex]
So, the answer will be:
The number of cases of pies to maximize the profit = 75
The maximum profit = $5625
