Suppose that the revenue​ R, in​ dollars, from selling x cell​ phones, in​ hundreds, is

Question

Suppose that the revenue​ R, in​ dollars, from selling x cell​ phones, in​ hundreds, is

R(x)=−1.3x^2+272x. The cost​ C, in​ dollars, from selling x cell​ phones, in​ hundreds, is C(x)=0.02x^3−2x^2+65x+600.



a) Find the profit​ function, P(x)=R(x)−C(x).

​(b) Find the profit if x=24 hundred cell phones are sold.

​(c) Interpret ​P(24)

Answer 1

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Answer 2

a) Find the profit​ function, P(x)=R(x)−C(x).

(1.3x^2+272x)-(0.02x^3-2x^2+65x+600)

P(x)=-0.02x^3+3.3x^2+207x-600

​(b) Find the profit if x=24 hundred cell phones are sold.

P(24)=-0.02(24)^3+3.3(24)^2+207(24)-600

P(24) = 5992.32

​(c) Interpret ​P (24)

You are making a profit at P (24) because your number is positive. A negative number would mean you are losing money.