Financial Gain Analysis of a Pen Company

Question:

A company makes pens. They sell each pen for $9. Their revenue is represented by R=9x. The cost to make the pens is $1 each with a one-time start-up cost of $4000. Their cost is represented by C=1x+4000. a) Find the profit, P,(P=R−C) when the company sells 1000 pens.

Options:

A. 13000

B. -3000

C. 4000

D. 9000

E. -9000

b) Find the number of pens they need to sell to break even (when R=C).

Options:

A. 4000

B. 445

C. 500

D. 572

Answer:

Profit is a financial term that refers to the amount of money or financial gain obtained by a business or individual after deducting expenses from revenue. The correct option for a is C) 4000 and for b is C.

To find the profit (P) when the company sells 1000 pens, we can use the formula:

P = R - C, where R represents revenue and C represents a cost.

Given:

- Revenue per pen (R) = $9

- Cost per pen (C) = $1

- One-time start-up cost (C) = $4000

- Number of pens sold (x) = 1000

First, let's calculate the revenue:

Revenue (R) = Revenue per pen (R) * Number of pens sold (x)

R = $9 * 1000 = $9000

Next, let's calculate the cost:

Cost (C) = Cost per pen (C) * Number of pens sold (x) + Start-up cost

C = $1 * 1000 + $4000 = $1000 + $4000 = $5000

Now, we can calculate the profit:

Profit (P) = Revenue (R) - Cost (C)

P = $9000 - $5000 = $4000

Therefore, the profit (P) when the company sells 1000 pens is $4000. The correct option is C) 4000.

b) Number of pens needed to break even (when R = C):

To find the break-even point, we need to set the revenue (R) equal to the cost (C) and solve for x.

Given, R = 9x and C = 1x + 4000

At the break-even point, R = C:

9x = 1x + 4000

Now, let's solve for x:

9x - 1x = 4000

8x = 4000

x = 4000 / 8

x = 500

So, the company needs to sell 500 pens to break even (when revenue equals cost). The correct option is C.