At Allied electronics, production has begun on x-15 computer chip. The total revenue function is given by. R(x)=47x-0.3x^2 and the total cost function is given C(x)=8x+16, where x represents the number of boxes of computer chip produced.

Question

A. Find the profit function in P(x)=R(x)-C(x)

Find the profit for 100 items produced

How many items do you have to produce to maximize the profit.

Thanks for your help.

Answer 1

A. They've told you what P(x) is:
P(x) = R(x)-C(x)
= 47x-.3x^2 - (8x+16)
= -.3x^2 + 39x - 16

Now , that's just a parabola, and you know that the parabola ax^2+bx+c has its vertex at x = -b/2a, so

max profit P(x) occurs at
x = -39/-.6 = 65