SOLUTION: The cost function for a certain company is C = 50x + 600 and the revenue is given by R = 100x − 0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equati

Algebra ->  Coordinate-system -> SOLUTION: The cost function for a certain company is C = 50x + 600 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 1124409: The cost function for a certain company is
C = 50x + 600 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 $600.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

C+=+50x+%2B+600 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-%2850x+%2B+600%29
P=100x+-0.5x%5E2-50x+-+600
P=-0.5x%5E2%2B50x++-+600

find two values of x+(production level) that will create a profit of $600:

600=-0.5x%5E2%2B50x++-+600
0.5x%5E2-50x%2B600%2B600=0+
0.5x%5E2-50x%2B1200=0+
0.5%28x%5E2-100x%2B2400%29=0+
0.5%28x%5E2-40x-60x%2B2400%29=0+
0.5%28%28x%5E2-40x%29-%2860x-2400%29%29=0+
0.5%28x%28x-40%29-60%28x-40%29%29=0+
0.5+%28x+-+60%29+%28x+-+40%29+=+0+
since 0.5%3C%3E0, equation will be zero if %28x+-+60%29++=+0+ or ++%28x+-+40%29+=+0+
if %28x+-+60%29++=+0+->x=60
if ++%28x+-+40%29+=+0+->x=40
so, the values of x (production level) that will create a profit of $600 are x=40 and x=60