A manufacturer has monthly cost of 60,000 and a production cost of 10$ for each unit produced. The product sells for $15/unit. a. What is the cost function.
b. What is the revenue function.
c. What is the profit function.

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

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

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.

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