at what rate is the supply changing?

Question

Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation.

$ 625p^2 - x^2 =100$

If 28000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 8¢/carton/week, at what rate is the supply changing? (Round your answer to the nearest whole number.) (Hint: To find the value of p when x = 28, solve the supply equation for p when x = 28.)
cartons per week.

Answer 1

First, when x = 28, p = square root of (884/625) = 1.1893

 

dx/dt = 625 (p/x) (dp/dt) = 625(1.1893)/28•(-0.08) =

-2.1237

Round as the instructor suggests, at the end of these calculations.  In other words, supply decreasing at about 2,124 cartons/week.