Problema Solution

Suppose the quantity demanded weekly of the Super Titan radial tires is related to its unit price by the equation

p + x2 = 256

where p is measured in dollars and x is measured in units of a thousand. How fast is the quantity demanded weekly changing when

x = 11,

p = 135,

and the price per tire is increasing at the rate of $2/week?

Answer provided by our tutors

We need to find dx/dt when dp/dt = 2, x = 11 and p = 135

Differentiate p + x^2 = 256:

dp/dx +2x*(dx/dt) = 0

2 + 2*11(dx/dt) = 0

22 (dx/dt) = - 2

dx/dt = -2/22

dx/dt = - 1/11

dx/dt = - 0.091

Since x is measured in thousands we have 0.091*1000 = 91 units per week.