The monthly cost C of producing x widgets in dollars is mode

The monthly cost C of producing x widgets (in dollars) is modeled by the function shown below. C(x) = 2500 + 4.8 x + 0.002 x^2 In this model 2500 represents fixed monthly costs and 4.8 is the individual cost of each unit being produced. The term 0.002x^2 represents additional costs that are significant only when the production level x is large. Such costs might include additional machinery, time-and-a-half pay, etc. If the maximum monthly cost the company can sustain is $10, 500, determine the maximum production level. Round your answer down to the next whole number.

Solution

Answer :

The monthly cost c of produce x widgets(in dollars) is modeled by the function

C(x) = 2500 + 4.8x + 0.002x² ------------------ ( 1 )

The maximum monthly cost the company can sustain is $ 10,500

Substitute C(x) = 10,500 in ( 1 ) we get

10,500 = 2500 + 4.8x + 0.002x²

0.002x² + 4.8x - 8000 = 0

dividing by 0.002 on both sides of the equation , we get

x² + 2400x - 4,000,000 = 0

Now solve for x we get x = 156-46