Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollar

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.

If 16000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 4¢/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 = 16, solve the supply equation for p when x = 16.)
______ cartons per week.

Explanation / Answer

First solve for p.

You get 625p2-x2=100

Plug in 16 for x to get p

625 p2 - 256 =100

p=0.754

Implicitly differentiate

1250p *dp/dt -2x dx/dt=0

1250(0.754) (0.04) -2(16)dx/dt=0

37.7 -32(dx/dt)=0

You get -32(dx/dt)=-37.7

dx/dt=1.178

Multiply that by 1000 and it will be 1178.

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