Thread: Desperately need help

If the demand function for a product is given by price p=1200-150x and the cost function is given by C(x)=900x-4X^3 find the following:

A. the profit function

B. the number of units which produce the maximum profit

C. the maximum profit

D. the price which produces this maximum profit.

Originally Posted by sempiternal_athena

If the demand function for a product is given by price p=1200-150x and the cost function is given by C(x)=900x-4X^3 find the following:

A. the profit function

P(x) = x(p(x) - C(x))

Originally Posted by sempiternal_athena

B. the number of units which produce the maximum profit

solve for P'(x) = 0 and solve for x..

Originally Posted by sempiternal_athena

C. the maximum profit

substitute what you found in (B) to P(x)

Originally Posted by sempiternal_athena

D. the price which produces this maximum profit.

substitute what you found in (B) to p(x)

Thank you for your help, can u tell me if this is correct?
P(x) = x(p(x) - C(x))
P(x)=x(1200-150x^2-(900x-4X^3 )
A).P=1200x-150x^2-900x-4x^3= 4x^3-150x^3-300x
B.)P`=12x^2-300x^2-300= two answers 1.04356 and 23.9564
C.)1200(1.04356)-150(1.04356^2)-900x(1.04356)-4(1.04356^3)=154
D.)p(x)=1200-900(1.04356)=260.8

Originally Posted by sempiternal_athena

Thank you for your help, can u tell me if this is correct?
P(x) = x(p(x) - C(x))
P(x)=x(1200-150x^2-(900x-4X^3 )
A).P=1200x-150x^2-900x-4x^3= 4x^3-150x^3-300x (Although this last expression is correct.
B.)P`=12x^2-300x^2-300= two answers 1.04356 and 23.9564

take note of the red ones.. try checking it.. it will affect the answers in C and D..