Calculus Word Problem

Question

Suppose the number of CD players a retail chain is willing to sell per week at a price of p dollars is given by the function S(p)=50p/0.4p+6.

Find the supply and the instantaneous rate of change of the supply with respect to price when the price is 40 dollars.

S(40) =  90.90 players

S′(40) =  75/121 players/dollar

Use your previous answers to estimate the increase in supply if the price rises from 40 to 50 dollars. Round your answer to the nearest integer.

Supply increase ≈  ? players

I calculated 96 but its saying its wrong!

Answer 1

You calculated the total supply, i. e., an estimate for S(50). What the problem wanted was the increase in supply, i. e., S(50)-S(40). The answer to the problem should be 10 (50-40) times 75/121 (S'(40), which equals 6.