Question

The marginal profit in dollars on Brie cheese sold at a cheese store is given by Upper P prime (x )equals x (60 x squared plus 90 x )comma where x is the amount of cheese​ sold, in hundreds of pounds. The​ "profit" is minus​$50 when no cheese is sold.
a. Find the profit function.
b. Find the profit from selling 400 pounds of Brie cheese.

Answer 1

Answer:

Part A:

P(x)=15x^4+30x^3-50

Part B:

P(4)=$4270

Step-by-step explanation:

Part A:

In order to find the profit function P(x) we have to integrate the P'(x)

P'(x)=x(60x^2+90x)

P'(x)=60x^3+90x^2

$\int\limits {p'(x)} \, dx =\int\limits {60x^3+90x^2} \, dx$

P(x)=15x^4+30x^3+C

when x=0, C=-50

P(x)=15x^4+30x^3-50

Part B:

x=4

P(x)=15x^4+30x^3-50

P(4)=15*4^4+30*4^3-50

P(4)=$4270

Profit from selling 400 pounds is $4270