The American ChainMail Corporation has net profits given by the function

The American ChainMail Corporation has net profits given by the function P(x) = –.1x2 + 10x + c
in hundreds of dollars, where x is the number of full suits of armor sold. Each full suit of armor costs $5,000, so the revenue function is R = 5000x.

(a) Complete the profit function by choosing a constant from the following: Choose a fixed cost (16000)

The value of c will actually be negative in the above function.

(b) Build the function for the net profit margin, NPM = P/R, and apply the quotient rule to find the rate of change when 40 suits of armor are sold. Then, estimate the number of suits of armor that need to be sold so that the NPM increases by 10%.