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A firm has monthly average costs, in dollars, given by 40,000 X C = + 100 + X where x is the number of units produced per month. The firm can sell its product in a competitive market for $1700 per unit. It number of units that gives maximum profit. x = 550 Find the maximum profit. $ ​

User Adam Kiryk
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The maximum profit based on the units that give maximum profit is $537,498.50.

We can find the maximum profit using the cost and revenue functions.

Monthly average costs equation: C = 40,000/x + 100 + x

The number of units produced per month = x

Total production units per month that give maximum profit: x = 550

Competitive market selling price per unit = $1,700

Average cost, C = 40,000/550 + 100 + 550

= $722.73

Total cost = $397,501.50 ($722.73 x 550)

Total sales revenue = 1,700(550) = $935,000

Maximum profit = $537,498.50 ($935,000 - $397,501.50)

Thus, the maximum profit is $537,498.50.

Complete Question:

A firm has monthly average costs, in dollars, given by C = 40,000/x + 100 + x where x is the number of units produced per month. The firm can sell its product in a competitive market for $1700 per unit. The number of units that give maximum profit is x = 550 Find the maximum profit.

User Hexdreamer
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