The demand function for a commodity is Q = 6000 - 30P, with P the price and Q the number of units. Fixed costs are R 72 000 and the variable cost is R 60 per additional unit produced. Dtermine the price at which profit is a maximum and calculate the maximum profit.

melodykap

melodykap

Answered question

2021-01-04

The demand function for a commodity is Q = 6000 - 30P, with P the price and Q the number of units. Fixed costs are R 72 000 and the variable cost is R 60 per additional unit produced. Dtermine the price at which profit is a maximum and calculate the maximum profit.

Answer & Explanation

un4t5o4v

un4t5o4v

Skilled2021-01-05Added 105 answers

Revenue earned will be =Demand×Price Revenue=(600030P)×P
Total Cost = Fixed Cost + Variable Cost
Total Cost =72000+60(600030P)
Profit = Revenue - Total Cost
Profit = (600030P)P(72000+60(600030P))
Profit = - 30P2+7800P432000
Now we have a quadratic equation for Profit. Now its a simple case of maximum value in quadratic equation.
Maximum Value of quadratic equation is at x = b2a
At P = 7800230, we will get max profit
i.e. Price at which max profit, P = R 130
Maximum Profit = R 75000

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