What is the profit if 1000 were sold

Question

Suppose that it costs a company selling sewing patterns C(x) =800 +6.5x dollars to produce and sell x patterns a month. If the revenue obtained by selling x patterns is R(x) =10x − 0.002x^2, what is the profit equation? How much profit will be made if 1,000 patterns are produced and sold in May?

Answer 1

R(x)= 10x - 0.002x^2

C(x) = 800 + 6.5x

P(x) = R(x)-C(x) = 10x - 0.002x^2 - 800 - 6.5x

P(x) = 3.5x - 0.002x^2 -800

P(1,000) = 3.5(1000) - 0.002(1000)^2 - 800

= 3500 - .002(1,000,000) - 800

= 2700 - 2,000

= $700 = profit with 1,000 patterns sold in May

(maximum possible profit is with 875 patterns sold

3.5(875) -.002(875)^2 -800 = $731.25