Question

Effect of Price on Supply of Eggs

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.

625p² − x² =100

If 22000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 3¢/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 = 22, solve the supply equation for p when x = 22.)

cartons per week

Answer 1

we have

put x = 22 thousand,

now,

put p=966.64, x =22000 and dp/dt = -3,

the supply is decreases at rate of 82 cartons per week.