A clothing company has compiled data based on their records of annual jacket sales. They have found a relationship between the sales of one jacket and that jackets's price: q = -20s + 1200, where q = quantity sold and s = selling price of the item. The cost to produce each jacket is $10.

a. Using the Profit formula P = Total Revenue - Production Costs (in this case, P = sq - 10q), write an equation that could be used to find the selling price, s, that produces the maximum profit.

(Hint: Take the equation for q and substitute it into the equation for P, then simplify.)

b

Question

A clothing company has compiled data based on their records of annual jacket sales.  They have found a relationship between the sales of one jacket and that jackets's price: q = -20s + 1200, where q = quantity sold and s = selling price of the item.  The cost to produce each jacket is $10.

 

a.  Using the Profit formula P = Total Revenue - Production Costs (in this case, P = sq - 10q), write an equation that could be used to find the selling price, s, that produces the maximum profit.

(Hint: Take the equation for q and substitute it into the equation for P, then simplify.)

 

b

anonymous · Answer

b.  Using that equation, what selling price should they set to maximize profit?

(Hint: Think about the general shape of the graph from your answer in Part A.  What part of the graph represents the maximum?  How do you find it?)