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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