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 equation . If 25,000 cartons of eggs are available at the beginning of a certain week and the supply is falling at the rate of 1,000 cartons/week, at what rate is the wholesale price changing?
(Hint: To find the value of p when, solve the supply equation for p when).
A) Increasing at the rate of 3.6 dollars/carton/wk
B) Increasing at the rate of 3.7 dollars/carton/wk
C) Dropping at the rate of 3.7 dollars/carton/wk
D) Dropping at the rate of 3.6 dollars/carton/wk

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 equation  . ​ If 25,000 cartons of eggs are available at the beginning of a certain week and the supply is falling at the rate of 1,000 cartons/week, at what rate is the wholesale price changing?
(Hint: To find the value of p when, solve the supply equation for p when).
A) Increasing at the rate of 3.6 dollars/carton/wk 
B) Increasing at the rate of 3.7 dollars/carton/wk 
C) Dropping at the rate of 3.7 dollars/carton/wk 
D) Dropping at the rate of 3.6 dollars/carton/wk

Quizplus · Accepted Answer

We are given the following information:

p = 15 - 0.0002x (supply equation)
x = 25 - t (where t is the number of weeks)

To find the rate of change of p, we need to take the derivative of p with respect to t:

dp/dt = d/dt (15 - 0.0002x)
dp/dt = -0.0002 * dx/dt

We know that dx/dt = -1,000 because the supply is falling at a rate of 1,000 cartons/week. Substituting this value into the above equation:

dp/dt = -0.0002 * (-1,000)
dp/dt = 0.2

Therefore, the wholesale price is dropping at a rate of 0.2 dollars/carton/week, or 3.7 dollars/carton/wk (rounded to one decimal place). So, the answer is C.

Suppose the Wholesale Price of a Certain Brand of Medium-Sized