Originally Posted by

**thelostchild** What you want to do is find the profit, subject to there being a positive demand (price<90) which would be

Profit=Revenue per week - Cost per week

$\displaystyle

P=pq-30q

$

$\displaystyle

P=p(90-p)^2-30(90-p)^2

$

$\displaystyle

P=p^3-210p^2+13500p-243000

$

Find stationary values by taking the first derivative of the profit function and setting it to 0, remembering the above condition then confirm which of the answers is a maximum by finding which would make the second derivative negative