Question

A retailer has been selling 400 tablet computers a week at $350 each. the marketing department estimates that an additional 80 tablets will sell each week for every $10 that the price is lowered. find the demand function.

Answer 1

d(p) = 3200 - 8p The demand function that the marketing depart is specifying is a simple linear equation. So it will be of the form d = ap + b where d = demand for tablets p = price of tables a = slope of demand b = y intercept So let's calculate the slope first. We already have one point where price = 350 and demand = 400. We can easily create a second point by subtracting 10 from the price and increasing demand by 80, so the second point is price = 340, demand = 480. Now let's calculate a a = (480 - 400)/(340 - 350) a = 80/(-10) a = -80/10 a = -8/1 a = -8 So our demand function now looks like d = -8p + b Let's now solve for b, then plug in the known price and sales figures and calculate. So: d = -8p + b d + 8p = b 400 + 8*350 = b 400 + 2800 = b 3200 = b So our final demand equation is d = -8p + 3200 Making it a function is d(p) = 3200 - 8p