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.
Accepted Solution
A:
Answer:Part A:P(x)=15x^4+30x^3-50Part B:P(4)=$4270Step-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[tex]\int\limits {p'(x)} \, dx =\int\limits {60x^3+90x^2} \, dx[/tex]P(x)=15x^4+30x^3+Cwhen x=0, C=-50P(x)=15x^4+30x^3-50Part B:x=4P(x)=15x^4+30x^3-50P(4)=15*4^4+30*4^3-50P(4)=$4270Profit from selling 400 pounds is $4270