1. In this problem, we analyze the profit found for sales of decorative tiles. A
ID: 3105880 • Letter: 1
Question
1. In this problem, we analyze the profit found for sales of decorative tiles. 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 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. Hint: Write your answer in the form
p = mx + b.
b. 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 quantity of the product sold, x, by the demand equation, p.
Explanation / Answer
a. Two points: (52, 10), (42, 20) slope = (20 - 10)/(42 - 52) = 10/-10 = -1 Point slope equation: (p - 10) = -1(x - 52) p - 10 = -x + 52 p = -x + 62 b. R = xp = x(-x + 62) R = -x^2 + 62x
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