Question

1) After the rise in popularity of the Croc shoe, a competitor brand will launch in January called “Srocs.” The company spends $9 to manufacture each pair of Sroc shoes. They also spend $8,000 on their Sroc-making machine and $4,000 on ads. One of the founders wants to sell each pair for $49 because that is the retail price for Crocs, but the other founder says they should sell the Srocs for $39.Write an equation for the company’s costs:Determine which price option you would choose and why.How much of the product must be sold to break even (using your chosen selling price)?

Answer 1

Company's costs:

Sroc's making machine = $8000

Ads = $4000

For each manufactured pair of Sroc shoes = $9

We add them to find the cost equation in terms of x manufactured pair of Srocs:

`\begin{gathered} C(x)=8000+4000+9x \\ \\ \Rightarrow C(x)=9x+12000 \end{gathered}`

There are two options for the selling price:

`\begin{gathered} P_1(x)=49x \\ P_2(x)=39x \end{gathered}`

We use each of them to find out how many Srocs we need to sell in order to have a null profit:

`\begin{gathered} 49x=9x+12000 \\ 40x=12000 \\ x=300 \end{gathered}`
`\begin{gathered} 39x=9x+12000 \\ 30x=12000 \\ x=400 \end{gathered}`

As we can see, we need to sell only 100 pairs of Srocs more to recover the investment. Therefore, we choose the selling price P₂:

`\text{ Selling price: \$39}`

Finally, we have already found how much of the product must be sold to break even:

`\text{ Answer: 400 pairs of Srocs}`