An electronic toy company has compiled data based on their records of annual sales. they have found a relationship between the sales of one toy and that toy's price: q = -5s + 1300, where q = quantity sold and s = selling price of the item. The cost to produce each toy is $80.
a. Using the Profit formula P = Total Revenue - Production Costs (in this case, P = sq - 80q), 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

An electronic toy company has compiled data based on their records of annual sales.  they have found a relationship between the sales of one toy and that toy's price: q = -5s + 1300, where q = quantity sold and s = selling price of the item.  The cost to produce each toy is $80.
a.  Using the Profit formula P = Total Revenue - Production Costs (in this case, P = sq - 80q), 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?)