Find the minimum value for avc – Managerial Economics

Assume that the manager of a company operating in competitive market has estimated the company’s average variable cost function to be AVC=4000-5Q+0.002Q^2

Total fixed cost is $62500. The firm across the street is charging $1000 per unit that they sell.
a. What is the minimum value for AVC?
b. How much output should the firm produce in the short run?
c. How much profit will the firm earn?

Hint: if we face the following quadratic equation: ax^2+bx+c=0, then we can find x using this formula
x=(-b+-(b^2-4ac))/2a.
Use the largest number as your solution

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