Question

A company makes pens. They sell each pen for $ 6

Answer 1

a. -3,000

b. 1,750

Step-by-step 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:

`\begin{gathered} Profit=Revenue-Cost \\ \text{For the making of 1,000 pens, it means: }x=1,000 \\ Revenue=6\cdot x=6*1,000 \\ Revenue=\text{\$}6,000 \\ Cost=2\cdot x+7,000 \\ Cost=2*1,000+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}`

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:

`\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=(7,000)/(4) \\ x=1,750 \\ \\ \therefore x=1,750 \end{gathered}`

Hence, the breakeven occurs when the company has made 1,750 pens