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.)

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.)

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?)

If someone could please help me and walk me through it instead of simply giving me the answer that would be great. Thank you in advance!