A fur dealer finds that when coats sell for $ 3200 , monthly sales are 60 coats. When the price increases to $ 3550 , the demand is for 30 coats. Assume that the demand equation is linear.

(a) Find the demand and revenue equations (in terms of , the number of coats sold monthly).

The demand equation is p=

the revenue equation is r(x)=

(b) If overhead is $ 4000 per month and the production cost per coat is $ 1500 , find the cost equation and the profit equation.

The cost equation is c(x)=
and the profit equation p(x)=

(c) Find the level of production that maximizes profit

Question

A fur dealer finds that when coats sell for $ 3200 , monthly sales are 60 coats. When the price increases to $ 3550 , the demand is for 30 coats. Assume that the demand equation is linear.

(a) Find the demand and revenue equations (in terms of , the number of coats sold monthly).

The demand equation is p=

the revenue equation is r(x)=

(b) If overhead is $ 4000 per month and the production cost per coat is $ 1500 , find the cost equation and the profit equation.

The cost equation is  c(x)=
and the profit equation p(x)=


(c) Find the level of production that maximizes profit