The FeatureRich Software Company sells its graphing program, Dogwood, with a volume discount. If a customer buys x copies, then that customer pays . It costs the company to develop the program and to manufacture each copy. If just one customer were to buy all the copies of Dogwood, how many copies would the customer have to buy for FeatureRich Software s average profit per copy to be maximized?
A)8,000 copies
B)20,000 copies
C)44,000 copies
D)40,000 copies
E)10,000 copies

Question

The FeatureRich Software Company sells its graphing program, Dogwood, with a volume discount. If a customer buys x copies, then that customer pays  . It costs the company  to develop the program and  to manufacture each copy. If just one customer were to buy all the copies of Dogwood, how many copies would the customer have to buy for FeatureRich Software s average profit per copy to be maximized?
A)8,000 copies 
B)20,000 copies 
C)44,000 copies 
D)40,000 copies 
E)10,000 copies

Quizplus · Accepted Answer

Let's say the customer buys x copies. Then the amount paid by the customer would be 11ebfe6a_2cd5_ce92_96cc_db0004d4ddc9_TBX8650_11x.

The profit made by the company would be the revenue earned minus the total cost. The revenue earned would also be the amount paid by the customer, which is 11ebfe6a_2cd5_ce92_96cc_db0004d4ddc9_TBX8650_11x. The total cost would be the cost of development plus the cost of manufacturing all the copies, which is 11ebfe6a_2cd5_ce93_96cc_032d00d3c3d8_TBX8650_11 + 11ebfe6a_2cd5_ce94_96cc_a1dec10634aa_TBX8650_11x.

So the profit made by the company would be:

profit = 11ebfe6a_2cd5_ce92_96cc_db0004d4ddc9_TBX8650_11x - (11ebfe6a_2cd5_ce93_96cc_032d00d3c3d8_TBX8650_11 + 11ebfe6a_2cd5_ce94_96cc_a1dec10634aa_TBX8650_11x)

Simplifying this, we get:

profit = 11ebfe6a_2cd5_ce95_96cc_58eec8e2f1b9_TBX8650_11x - 11ebfe6a_2cd5_ce93_96cc_032d00d3c3d8_TBX8650_11 - 11ebfe6a_2cd5_ce94_96cc_a1dec10634aa_TBX8650_11x

To maximize the average profit per copy, we need to maximize the profit. So let's take the derivative of the profit with respect to x and set it to zero:

11ebfe6a_2cd5_ce95_96cc_58eec8e2f1b9_TBX8650_11 - 11ebfe6a_2cd5_ce94_96cc_a1dec10634aa_TBX8650_11 = 0

Solving for x, we get:

x = 40,000

So the customer would have to buy 40,000 copies for FeatureRich Software's average profit per copy to be maximized. Therefore, the answer is D.

The FeatureRich Software Company Sells Its Graphing Program, Dogwood, with a Volume