A company can produce a doll at a cost of $5 per doll.

Question

A company can produce a doll at a cost of $5 per doll. When the company sells the dolls at a price of $40, they can sell 400 dolls each week. It is estimated that for every $0.50 decrease in the price, they can sell 20 more dolls. Find the price that will maximize the profit for the company.

Answer 1

Hello Leah,

 

When the company makes each doll at $5 and sells each doll at $40, they make a $35 profit on each doll. At this price, the company can sell 400 dolls each week, so their weekly profit y (in dollars) at this price is:

 

     y = 35 · 400

 

Each time the company decreases the selling price by $0.50, they can sell 20 more dolls. We can write this into our profit equation as:

 

     y = (35 - 0.50x) · (400 + 20x)

 

where x is the number of times the company reduces the selling price of their dolls. Let's FOIL this out, combine like terms, and rearrange:

 

     y = 35 · 400  +  35 · 20x  -  0.50x · 400  -  0.50x · 20x

     y = 14000 + 700x - 200x - 10x²

     y = -10x² + 500x + 14000

 

At this point, there are two different ways to find the maximum profit for the company.

 

1) You could fill out a T-chart with x-values of 0, 1, 2, 3... until you find where the y-values start decreasing. This is as simple as plugging in values for x and finding what y values come out of the above equation.

 

2) You can recognize that the above equation is the equation for a parabola, then solve for the maximum value of y by using what you've learned about parabolas.

 

My guess is that your teacher wants you to use a T-chart to find the answer. Remember that the question asks for the selling price of the dolls, so be sure to use (40 - 0.50x) when giving your final answer!

 

I hope this has helped!