Question

Suppose a firm that produces pints of gourmet ice cream has monthly fixed costs of $12,000. The variable costs come to $1.50 per pint produced. (for up to 40,000 pints/month) and the firm sells each pint of ice cream for $3. Find the firm's profit function.

Answer 1

$48,000

Step-by-step explanation:

The Profit function shows the relationship between the total costs and total revenue accrued in a business. It is given by the formula;

Product Function=Total revenue - Total costs.

The fixed costs in a business are those expenses that must be taken care of no matter the level of production. Variable costs however are dependent on the output of the company.

For the firm producing Gourmet ice-cream,

Total Revenue= $3*40000 pints/month = $120,000

Total costs=Fixed cost +Variable costs

= $12,000 + $40000*(1.5)

= $12,000 + $60,000

= $72000

Therefore,

Product Function= $120,000 - $72000

= $48000

Answer 2

P(x)=1.5x-12,000

Step-by-step explanation:

The profit function equation is:

P(x) = R(x) - C(x)

P(X)= Profit

R(x)= Revenue= 3x

C(x)= cost= fixed costs+variable costs=12,000+1.50x

x= number of pints of ice cream

Then, you can replace the equation with the information given:

P(x)=3x-(12,000+1.50x)

P(x)= 3x-12,000-1.5x

P(x)=1.5x-12,000

According to this, the answer is that the firm's profit function is P(x)=1.5x-12,000.