Question

Find the profit maximizing level of output if demand
function is x = 240 - 10p and average cost function
is AC = 10 + x/25, where x denotes the units of output
and p represents price.​

Answer 1

Please find the solution

Answer 2

Answer:

The profit maximizing level of output is 50 units.

Step-by-step explanation:

Using the concept of cost, revenue and profit.

Average Cost: Average cost is the cost per unit of a product manufactured.

Revenue: Revenue is the income that is obtained by selling a product at a price.

Profit: Financial gain that is obtained from the revenue after the costs are covered.

Given information, x is units of output and p is the price.

Demand function is x = 240 - 10p

Average cost is AC = 10 + x/25

As we know, Profit = Revenue - Cost

Revenue = Price of unit * Number of units sold (Demand)

Revenue = p * x

$Revenue = x * (\frac{240-x}{10} )$

Cost = Average cost * Number of units (Demand)

$Cost = (10+\frac{x}{25}) *x\\\\Cost = 10x+\frac{x^{2} }{25}$

Profit = Revenue - Cost

$Profit = \frac{240x-x^{2} }{10} - (10x+\frac{x^{2} }{25})\\ \\Profit = \frac{5(240x-x^{2} )}{50} -(\frac{500x+2x^{2} }{50})$

To find the profit maximizing level of output, differentiate profit equation with output,x

$Profit = (700x - 7x^{2} )/50\\\\\frac{d(Profit)}{dx} = \frac{\frac{d(700x-x^{2}) }{50} }{dx} = 0\\\\700-2x = 0\\\\x = 50$

Therefore, the profit maximizing level of output is 50 units.

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