Question

Theodore and Sarah have a small business selling custom-made T-shirts. They currently sell 200 shirtsper month and charge $14 per T-shirt. Sarah thinks they can increase their revenue by increasing theirselling price, but Theodore knows from experience that each $1 increase in price will decrease thenumber of T-shirts they sell by 9 shirts per month. Find an expression for the total monthly revenueTheodore and Sarah's business can generate if they change the selling price of their T-shirts. Let xrepresent the number of $1 increases in the price of the T-shirts.

Answer 1

We are told that there are currently 200 shirts

If each shirt is sold for $14, then the total revenue will be

`200*\text{ \$14= \$2800}`

Therefore, we can conclude that the revenue formula is

`\text{Revenue}=\text{Number of shirts}* unit\text{ cost}`

From the question, we are told

`\begin{gathered} \text{Number of shirts reduces by 9 for every one dollar increment} \\ \text{Thus, we have} \\ 200-9x \end{gathered}`

Similarly, the cost will be

`x+14`

Therefore, the total revenue will be defined by

`\begin{gathered} \text{Total }Revenue=\text{Revenue}=\text{Number of shirts}* unit\text{ cost=}\lbrack(x+14)*(200-9x)\rbrack \\ \text{Total }Revenue=\lbrack(x+14)*(200-9x)\rbrack \end{gathered}`