Amanufacturer has a monthly fixed cost of $70,000 and a production cost of $13 for each unit produced. the production sells for $20 per unit.
a) what is the profit function?

b) what is the marginal cost?

c) how many units should be sold to break even?

d) compute the profit or loss corresponding to production levels of 2000 units.

e) if the manufacturer sold 15000 units of the product what was the average cost per unit?

Please see below.

Explanation:

a) Profit Function

A profit function is a mathematical relationship between a firm's total profit and output. It equals total revenue minus total costs, and it is maximum when the firm's marginal revenue equals its marginal cost.

b) Marginal Cost

A conventional marginal cost is incremented by one unit; that is, it is the cost of producing one more unit of a good. Intuitively, marginal cost at each level of production includes the cost of any additional inputs required to produce the next unit.

c) Break-even point per unit

= Fixed Cost / Contribution margin per unit

where as;

Fixed Cost = $70000

Contribution margin per unit = (Sale price per unit - production cost per unit)

             = ($20 - $13)

             = $7

Break-even point per unit = 70000 / 7

         = 10000

So, the manufacturer has to sell at least 10,000 units in order to cover it's fixed and production costs.

d) Production Level of 2000 units

Sales price per unit = $20

Production cost per unit = $13

Gross Profit / (Loss) per unit = $7

So if, 2000 units are produced,

Gross Profit / (Loss) = 7(2000)

Gross Profit / (Loss) = 14000

Net Profit / (Loss) = Gross Profit - Fixed Cost

Net Profit / (Loss) = 14000 - 70000

Net Profit / (Loss) = -56000

Hence to production level of 2000 units corresponds to a loss of $56,000

e) Average cost per unit

Total cost of production / the number of units produced

where as ;

Total cost of production = Fixed Cost + Production Cost

Total cost of production = 70000 + (15000)13

Total cost of production = 70000 + 195000

Total cost of production = 265000

So,

Average cost per unit = 265000 / 15000

Average cost per unit = $17.67

Average cost per unit = $18

Hence to production level of 15000 units corresponds to an average cost of $18 per unit.