SOLUTION: The cost function for a certain company is C = 50x + 400 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 + 400 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 1182146: The cost function for a certain company is
C = 50x + 400
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 $400

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
C+=+50x+%2B+400
R+=+100x+-0.5x%5E2
find profit:
P=R-C
P=100x+-0.5x%5E2-%2850x+%2B+400%29
P=100x+-0.5x%5E2-50x+-+400
P=+-0.5x%5E2%2B50x+-+400
if P=400
400=+-0.5x%5E2%2B50x+-+400
0=+-0.5x%5E2%2B50x+-+400-400
0=+-0.5x%5E2%2B50x+-+800....factor
0=+-0.5%28x%5E2-100x+%2B1600%29
0=+-0.5%28x%5E2-20x+-80x%2B1600%29
0=+-0.5%28%28x%5E2-20x%29+-%2880x-1600%29%29
0=+-0.5%28x%28x-20%29+-80%28x-20%29%29
0+=+-0.5+%28x+-+80%29+%28x+-+20%29
solutions:
x=80
x=20