Class 1. Q.9

The Market Research department of a company recommended to the Management that the company manufacture and market a promising new product. After an extensive survey the research department backed up the recommendation with the demand equation x=f(p)=6000-30p, where x is the number of the units that retailers are likely to buy per month at $\$p$ per unit. From the financial department the cost equation was obtained C=g(x)=72000+60x, $\$72000$ is the fixed cost (tooling and overhead) and $\$60$ is the variable cost per unit (materials, labor, marketing, etc.) .

(a)

Express the cost function as a function of p.

(b)

Find the demand when the price per unit is $\$10$

(c)

Find the cost when the price per unit is $\$10$. Also find the cost when the price per unit is $\$5$.