Acompany manufacturers and sells x electric drills per month. the monthly cost and price-demand equations are c(x)=6+70x, p=190−x30,0≤x≤5000. (a) find the production level that results in the maximum profit.

The answer is: 1,800 electric drills per month

Explanation:

C(x) = 60,000 + 70x

p = 190 - (x / 30)

0 ≤ x ≤ 5000

To determine the production level that maximized profit, we need to solve the following equation:

profit = px - c

profit = [190 - (x / 30)]x - (60,000 + 70x)

profit = 190x - x²/30 - 60,000 - 70x

profit = 120x - x²/30 - 60,000

profit' = 120 - x/15

0 = 120 - x/15

x/15 = 120

x = 1,800

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