A manufacturer sells each of his TV sets for $85. The cost C (in dollars) of manufacturing and selling x TV sets per week is C = 1500 + 10x + 0.005x2. If at most 10,000 sets can be produced per week, how many sets should be made and sold to maximize the weekly profit?

Question

Mathematics

Alexis Roth

8 September, 05:24

A manufacturer sells each of his TV sets for $85. The cost C (in dollars) of manufacturing and selling x TV sets per week is C = 1500 + 10x + 0.005x2. If at most 10,000 sets can be produced per week, how many sets should be made and sold to maximize the weekly profit?

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Cantu · Answer 1

Answer: You should produce all 10,000 TV sets to reach the maximum profit.

If you graph the equation for the profit (below), you will see that the function is increasing on the entire interval from 0 to 10,000.

P = 85x - (1500 + 10x + 0.005x^2)

Therefore, the maximum project would be at the end of the interval, or 10,000 TV units.