SOLUTION: The cost function for a certain company is C = 40x + 800 and the revenue is given by R = 100x − 0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equati

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The cost function for a certain company is C = 40x + 800 and the revenue is given by R = 100x − 0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equati      Log On


   

Question 1207491: The cost function for a certain company is
C = 40x + 800
and the revenue is given by
R = 100x − 0.5x2.
Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $800.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
C+=+40x+%2B+800
and the revenue is given by
R+=+100x+-0.5x%5E2
Recall that profit is revenue minus cost.
P=R-C
P=100x+-0.5x%5E2-%2840x+%2B+800%29
P=100x-0.5x%5E2-40x+-+800
P=+-+0.5x%5E2%2B60x+-+800

two values of x+(production level) that will create a profit of $800:

800=+-0.5x%5E2%2B60x+-+800
800%2B0.5x%5E2-60x+%2B+800=0
0.5x%5E2-60x+%2B+1600=0
0.5%28x%5E2-120x%2B3200%29=0
0.5%28x%5E2-40x-80x%2B3200%29=0
0.5+%28x+-+80%29+%28x+-+40%29+=+0

solutions:
x=40
x=80