The profit (p), in dollars, for a company is modeled by the function P(x)=-750xsquared+15,000x, where x is the number of items produced. For which values of x will the company lose money? a. x

Question

The profit (p), in dollars, for a company is modeled by the function P(x)=-750xsquared+15,000x, where x is the number of items produced. For which values of x will the company lose money? a. x<2 b. 2<x<=10 c. 10<=x<20 d. x>20

anonymous · Answer

C: x>20

P(x)= -750x^2 +15,000x = 0
x(-750x + 15000) = 0
x = 0 and x = 20 this divides the x axis into 3 'regions'
1st less than 0 impossible ... you cannot produce a negative number of items
2nd ...0 to 20
test x = 1 ... P is positive .. the company makes money if P is positive
3rd ... greater than 20
test x = 25 ... P is negative ... the company loses money

so x>20 is the answer