Answer:
a. -3,000
b. 1,750
Explanation:
We were given the following information:
A company makes pens:
Each pen is sold at $6 per unit
Revenue = 6 * x
Manufacture Cost = 2 * x
Start-up Cost = $7,000
Cost = Manufacture Cost + Start-up Cost = 2 * x + 7,000
Profit = Revenue - Cost
a) The profit is calculated for 1,000 pens as shown below:
[tex]\begin{gathered} Profit=Revenue-Cost \\ \text{For the making of 1,000 pens, it means: }x=1,000 \\ Revenue=6\cdot x=6\times1,000 \\ Revenue=\text{\$}6,000 \\ Cost=2\cdot x+7,000 \\ Cost=2\times1,000+7,000 \\ Cost=2,000+7,000 \\ Cost=\text{\$}9,000 \\ \\ Profit=6,000-9,000 \\ Profit=-\text{\$}3,000 \\ \\ \therefore Profit=-\text{\$}3,000 \end{gathered}[/tex]Hence, the profit is -3,000
b) We will calculate for the number of pens needed to be sold for the company to break even as shown below. We have:
[tex]\begin{gathered} \text{At breakeven: }Revenue=Cost \\ \Rightarrow6x=2x+7,000 \\ \text{We will calculate for the value of the variable ''x'':} \\ 6x=2x+7,000 \\ \text{Subtract ''2x'' from both sides, we have:} \\ 6x-2x=7,000 \\ 4x=7,000 \\ \text{Divide both sides by ''4'', we have:} \\ x=\frac{7,000}{4} \\ x=1,750 \\ \\ \therefore x=1,750 \end{gathered}[/tex]Hence, the breakeven occurs when the company has made 1,750 pens
