SOLUTION: The revenue achieved by selling x graphing calculators is figured to be x(32 - 0.2x) dollars. The cost of each calculator is $20. How many graphing calculators must be sold to make

Algebra ->  Functions -> SOLUTION: The revenue achieved by selling x graphing calculators is figured to be x(32 - 0.2x) dollars. The cost of each calculator is $20. How many graphing calculators must be sold to make      Log On


   

Question 242811: The revenue achieved by selling x graphing calculators is figured to be x(32 - 0.2x) dollars. The cost of each calculator is $20. How many graphing calculators must be sold to make a profit of at least $155.80?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Profit = Revenue - Cost, where Revenue is given, and Cost = $20 *(number of calculators)
Profit = x(32-0.2x)- 20x
32x-0.2x%5E2+-20x+%3E=155.8
-0.2x%5E2+%2B12x+-155.8%3E=0

Divide both sides by -0.2:
x%5E2-60x%2B+779%3C=0

Completing the square gives this:
x%5E2+-60x%2B900%3C=-779%2B900
%28x-30%29%5E2%3C=121

NOTE: The fact that 121 is a perfect square means that this problem COULD have been solved by factoring. However, factoring a number like 779 is a DIFFICULT thing to do!!!

The endpoints are at:
x-30=0%2B-11
x=30%2B-11
x=30%2B11=41 or x=30-11=19

Profit will be greater than this amount when x is between 19 and 41 units. Maximum profit will be at in the middle of this interval at x=30 units.

Graphing calculators and quadratic formula are alternate methods of solving this one. Let me know if you would like to see either of these methods.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus