Question

A manufacturer has monthly cost of 60,000 and a production cost of 10$ for each unit produced. The product sells for $15/unit.

Answer 1

Answer:

a. What is the cost function.

C(x) = 10x + 60,000

b. What is the revenue function.

R(x) = 15x

c. What is the profit function.

P(x) = R(x) - C(x) = 15x - 10x - 60,000 = 5x - 60,000

Compute the profit loss corresponding to production level of 10,000 and 14000.

10,000 units produced:

P(10,000) = 5(10,000) - 60,000 = 50,000 - 60,000 = -$10,000

14,000 units produced:

P(14,000) = 5(14,000) - 60,000 = 70,000 - 60,000 = $10,000

Answer 2

Answer:

1. There is a loss of $10,000 at the production level of 10,000.

2. There is a profit of $10,000 at the production level of 14,000.

Explanation:

From the question, we have:

a = Fixed cost = $60,000

b = Variable cost per unit = $10

P = price per unit = $15

Therefore, we have:

a. What is the cost function.

The cost function can be stated as follows:

C = a + bY ............................... (1)

Where;

C = total cost

a = Fixed cost = $60,000

b = Variable cost per unit = $10

Y = production level

Substituting the relevant values into equation (1), we have:

C = 60,000 + 10Y <--------------- Cost function

b. What is the revenue function.

The revenue function can be stated as follows:

R = P * Y ...................... (2)

Where;

R = Total revenue

P = price per unit = $15

Y = production level

Substituting the relevant values into equation (2), we have:

R = 15 * Y ........................... <------------------ Revenue function

c. What is the profit function.

The profit function can be stated as follows:

Profit (loss) = R - C .......................... (3) <------------------- Profit function.

1. Compute the profit loss corresponding to production level of 10,000

This implies that;

Y = 10,000

C = 60,000 + (10 * 10,000) = $160,000

R = 15 * 10,000 = $150,000

Profit (Loss) = $150,000 - $160,000 = ($10,000)

Therefore, there is a loss of $10,000 at the production level of 10,000.

2. Compute the profit loss corresponding to production level of 14,000

This implies that;

Y = 14,000

C = 60,000 + (10 * 14,000) = 200,000

R = 15 * 10,000 = $210,000

Profit (Loss) = $310,000 - $200,000 = $10,000

Therefore, there is a profit of $10,000 at the production level of 14,000.