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.