Minimum-Break Even Quantity, Max Revenue, Max Profit

Question

C(x) is the cost to produce x batches of widgets and R(x) is the revenue in thousands of $. C(x)= 3x + 32 and R(x) = -x² + 15x.

(a) Graph Both Functions.

(b) Find the minimum break-even quantity

(c) find the maximum revenue

(d) find the max profit

Answer 1

We need R to equal C or 3x + 32= 15x- x^2 or 12x-x^2 -32 = 0

Factoring we get (x-4)(8-x)=0 since x can't be negative this occurs when x=4