Q: Which of the following is the correct formula for linear depreciation per year?

$$\text{Depreciation} = \frac{\text{Initial Value} - \text{Salvage Value}}{\text{Useful Life}}$$

Question 1

A company sells a product for $$50 per unit. The cost to produce x$ units is given by C(x) = 20x + 500$. What is the profit function P(x$$)$?

Accepted Answer

$$P(x) = 50x - (20x + 500)$$

Question 2

If the revenue function is $$R(x) = 80x$$ and the cost function is $$C(x) = 60x + 1200$$, what is the break-even point?

Accepted Answer

$$x = 60$$

Question 3

Which of the following best describes the marginal cost?

Accepted Answer

The derivative of the cost function with respect to the number of units produced

Question 4

A machine is purchased for $$\10$$,000$$ and is expected to have a salvage value of $$\$$2,000$$ after 8 years. What is the annual linear depreciation?

Accepted Answer

$$\800$

Question 5

If the cost function is $$C(x) = 5x + 200$$ and the revenue function is $$R(x) = 15x$$, what is the profit when 30 units are sold?

Accepted Answer

$$P(30) = 250$$

Question 6

A company’s cost function is $$C(x) = 12x + 300$$ and its revenue function is $$R(x) = 20x. At $$what quantity $$x$$ does the company break even?

Accepted Answer

$$x = 37.5$$

Question 7

Which equation represents the point of equilibrium in terms of cost and revenue functions?

Accepted Answer

$$C(x) = R(x)$$

Question 8

If the marginal cost is $$MC(x) = 7$$, what does this mean in a real-world context?

Accepted Answer

Each additional unit produced costs $$\7$

Question 9

A company’s equipment depreciates linearly from $$\15$$,000$$ to $$\$$3,000$$ over 6 years. What is the value of the equipment after 4 years?

Accepted Answer

$$\7$$,000$

Question 10

If the cost function is $$C(x) = 10x + 400$$ and the revenue function is $$R(x) = 25x$$, what is the profit function?

Accepted Answer

$$P(x) = 15x - 400$$

Question 11

A company’s cost function is $$C(x) = 8x + 1200$$ and its revenue function is $$R(x) = 20x. $$What is the profit when 100 units are sold?

Accepted Answer

$$P(100) = 600$$

Question 12

Which of the following is the correct formula for linear depreciation per year?

Accepted Answer

$$	ext{Depreciation} = \frac{	ext{Initial Value} - 	ext{Salvage Value}}{	ext{Useful Life}}$$

Question 13

If the cost to produce $$x$$ units is $$C(x) = 6x + 900$$ and the marginal cost is constant, what is the marginal cost?

Accepted Answer

$$6$$

Question 14

A company’s revenue function is $$R(x) = 30x$$ and its cost function is $$C(x) = 18x + 600. $$What is the minimum number of units that must be sold to make a profit?

Accepted Answer

$$x = 60$$

Question 15

If the profit function is $$P(x) = 12x - 480$$, what is the break-even quantity?

Accepted Answer

$$x = 40$$

Question 16

A company’s cost function is $$C(x) = 9x + 1500$$ and its revenue function is $$R(x) = 15x. $$What is the profit when 200 units are sold?

Accepted Answer

$$P(200) = 300$$

Question 17

Which of the following statements is true about the break-even point?

Accepted Answer

It is the point where total revenue equals total cost

Question 18

A company’s equipment is purchased for $$\24$$,000$$ and depreciates linearly to $$\$$0$$ over 8 years. What is the book value after 5 years?

Accepted Answer

$$\9$$,000$

Question 19

If the cost function is $$C(x) = 7x + 350$$ and the revenue function is $$R(x) = 14x$$, what is the profit function?

Accepted Answer

$$P(x) = 7x - 350$$

Question 20

A company’s cost function is $$C(x) = 10x + 500$$ and its revenue function is $$R(x) = 20x. $$What is the profit when 80 units are sold?

Accepted Answer

$$P(80) = 300$$

Business Calculus: Core Economic Functions and Applications

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