Suppose you own a company that produces face-mask. The cost of makingLaTeX: x\:\:xface-mask is found using LaTeX: C\left(x ight)=0.25x^2+40x+1000\:\:C ( x ) = 0.25 x 2 + 40 x + 1000dollars. Also suppose you charge your customers $80 per mask.

a) Find the marginal cost, marginal revenue and marginal profit functions.

b) Find the revenue, profit, marginal revenue, marginal profit, if you have made 20 face-masks this month.

c) For which value ofLaTeX: x\:xis the marginal profit zero? Interpret your answer.