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Appendix-C-Solutions - Appendix C Solutions Retail...

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Appendix C Solutions Retail companies need to keep close track of their operations in order to maintain profitability. Often, the sales data of each individual product is analyzed separately, and this information can be used to help set pricing and other sales strategies. In this problem, we will analyze the profit found for sales of decorative tiles. 1. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research). a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Let x = the number of tiles sold per month. The following t-table shows points for the line: x = quantity p = price sold 42 20 52 10 To get the equation for the line, use (p-p 0 ) = m(x-x 0 ) m = 1 10 10 52 42 10 20 - = - = - - Using (x,p) = (42, 20), line equation is (p-20) = -1(x-42) p = 20 – x + 42 p = -x + 62 A company’s revenue is the amount of money that comes in from sales before business costs are subtracted. For a single product, you can find the revenue by multiplying the
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