Question

the profit (P), in dollars, for a company is modeled by the function P(x)=-750x^2+15000, where x is the number of items produced. for which values of x will the company lose money ?

Answer 1

P(x) = -750x^2 + 15000

If profit goes below zero, then the company will lose money,

therefore set P(x) = 0, then solve for x:

0 > -750x^2 + 15000
750x^2 > 15000
x^2 > 15000/750
x^2 > 20
x > 2sqrt{5} or 4.47

Since x can only be a positive, whole number, the company will start losing money only if they produce 5 items or more.

Answer 2

Notice that if they produce 1,2,3, or 4 items, they still make a profit. But when they produce the fifth item, they start losing money.