Question

For a certain company, the cost for producing x items is 35x+300 and the revenue for selling x items is 75x−0.5x^2
This is similar to Part b, but instead you need to solve the equation P=$15,000. Hint - the quadratic equation might be the easiest method for this part

How do I set up this equation?

Answer 1

The equation  set up is:

0.5x² - 40x + 15300 = 0

Cost, C(x) = 35x + 300

Revenue, R(x) = 75x - 0.5x²

Profit, P(x) = 15000

Profit = Revenue - Cost

P(x) = R(x) - C(x)

15000 = 75x - 0.5x² - (35x + 300)

15000 = -0.5x² + 40x - 300

0.5x² - 40x + 15000 + 300 = 0

The quadratic equation to get the number of items sold is shown below:

0.5x² - 40x + 15300 = 0

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