Question 1

Suppose the total cost function for producing x units is $$C(x) = 10,000 + 90x - 0.05x^2$. What is the marginal cost function?

Accepted Answer

$$C'(x) = 90 - 0.1x$$

Question 2

Given the cost function $$C(x) = 10,000 + 90x - 0.05x^2$, what is the marginal cost at a production level of 500 units?

Accepted Answer

$$40$$

Question 3

For the cost function $$C(x) = 10,000 + 90x - 0.05x^2$, what is the exact cost of producing the 501st unit?

Accepted Answer

$$39.95$$

Question 4

Which of the following best describes the relationship between marginal cost and the exact cost of producing one more unit?

Accepted Answer

Marginal cost approximates the exact cost of producing the next unit.

Question 5

A company’s price-demand equation is $$x = 10,000 - 1,000p. $$What is the price as a function of demand?

Accepted Answer

$$p = 10 - 0.001x$$

Question 6

Given the price-demand function $$p = 10 - 0.001x$$, what is the domain for $$x if $$both price and demand must be nonnegative?

Accepted Answer

$$0 \u003c x \u003c 10,000$$

Question 7

If the cost function is $$C(x) = 7,000 + 2x$$, what is the marginal cost and its interpretation?

Accepted Answer

Marginal cost is $$2$$, meaning each additional unit costs $$2 to $$produce.

Question 8

Given the revenue function $$R(x) = 10x - 0.001x^2$, what is the marginal revenue function?

Accepted Answer

$$R'(x) = 10 - 0.002x$$

Question 9

For the revenue function $$R(x) = 10x - 0.001x^2$, what is the marginal revenue at x = 5$$,000$$ units?

Accepted Answer

$$0$$

Question 10

If the cost function is $$C(x) = 7,000 + 2x$$ and the revenue function is $$R(x) = 10x - 0.001x^2$, what is the profit function?

Accepted Answer

$$P(x) = -0.001x^2$ + 8x - 7,000$$

Question 11

For the profit function $$P(x) = -0.001x^2$ + 8x - 7,000$$, what is the marginal profit function?

Accepted Answer

$$P'(x) = -0.002x + 8$$

Question 12

If the marginal profit at $$x = 4,000$$ units is $$0$$, what does this indicate about profit at this production level?

Accepted Answer

Profit does not change if production increases.

Question 13

Given the average cost function $$AC(x) = \frac{C(x)}{x}$$, what is the correct procedure to find the marginal average cost?

Accepted Answer

First find the average cost, then take its derivative.

Question 14

A company’s total cost for printing $$x$$ dictionaries is $$C(x) = 20,000 + 10x. $$What is the average cost per dictionary if 1,000 dictionaries are produced?

Accepted Answer

$$30$$

Question 15

If the marginal average cost at a production level of 1,000 dictionaries is $$-0.02$$, what does this mean?

Accepted Answer

Each additional dictionary produced reduces the per unit cost by about 2 cents.

Question 16

If the average cost for 1,000 dictionaries is $$30.00$$ and the marginal average cost is $$-0.02$$, estimate the average cost for 1,001 dictionaries.

Accepted Answer

$$29.98$$

Question 17

Which of the following is NOT a correct interpretation of the marginal cost function?

Accepted Answer

It is the total cost divided by the number of items produced.

Question 18

If the marginal revenue at a certain production level is negative, what does this imply about increasing production?

Accepted Answer

Increasing production will decrease total revenue.

Question 19

In the context of business calculus, what does the break-even point represent?

Accepted Answer

The production level where total revenue equals total cost.

Marginal Analysis in Business and Economics: Marginal Cost, Revenue, and Profit 2.7

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