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Mathematics
OpenStudy (anonymous):

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 ?

hero (hero):

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.

hero (hero):

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.

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