Question

The profit in dollars in producing x- items of some commodity is given by the equation P = - 37 x^2 + 1073 x - 7548 .
How many items should be produced to break even? (If there are two break-even points, then enter the smaller value of x. Your solution may not be an integer. Use your calculator for irrational square roots.)
How many items should be produced to maximize the profit?
What is the maximum profit? (You may need your calculator to compute the value.)

Answer 1

Profit = 0 is break even.

So solve for x in
P(x)=-37x²+1073x-7548 = 0
to give x=12 or x=17

The profit is given by the maximum of the P(x) function, which is located at x=(12+17)/2=15.5, or the maximum profit is
P(15.5). (substitute 15.5 for x and evaluate the profit).