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.