Question 1

Suppose the total cost of producing $$x$$ units is given by $$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

If $$C(x) is $$the total cost of producing $$x$$ items, which of the following best describes the relationship between marginal cost and the exact cost of producing one more item?

Accepted Answer

$$C'(x) \approx C(x+1) - C(x)$$

Question 5

A company’s price-demand equation is $$x = 10,000 - 1,000p. $$What is the domain of the function $$p = 10 - 0.001x$$?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

$$0$$

Question 9

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

Accepted Answer

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

Question 10

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 11

If the average cost function is $$\frac{C(x)}{x}$$, what is the correct way to find the marginal average cost?

Accepted Answer

First find the average cost, then take its derivative.

Question 12

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

Accepted Answer

$$30$$

Question 13

For $$C(x) = 20,000 + 10x$$, what is the marginal average cost at $$x = 1,000$$?

Accepted Answer

$$-0.02$$

Question 14

If the marginal average cost at $$x = 1,000 is$$ $$-0.02$$ and the average cost for 1,000 units is $$30$$, what is the estimated average cost for 1,001 units?

Accepted Answer

$$29.98$$

Question 15

Which of the following statements about marginal cost and marginal average cost is TRUE?

Accepted Answer

Marginal cost approximates the exact cost of producing the next item, but marginal average cost does not.

Question 16

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

Accepted Answer

Profit does not change if production increases from 4,000 units.

Question 17

A company’s revenue function is $$R(x) = 10x - 0.001x^2$. At what production level does the marginal revenue become zero?

Accepted Answer

$$x = 5,000$$

Question 18

If the cost function is $$C(x) = 10,000 + 150x - 0.2x^2$, what is the exact cost of producing the 121st bicycle?

Accepted Answer

$$101.80$$

Question 19

Given the same cost function $$C(x) = 10,000 + 150x - 0.2x^2$, what is the marginal cost at x = 120$?

Accepted Answer

$$102.00$$

Marginal Analysis in Business and Economics: Limits and the Derivative

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