Question

Suppose the quantity demanded weekly of the Super Titan radial tires is related to its unit price by the equation p + x2 = 225 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 = 6, p = 189, and the price per tire is increasing at the rate of $2/week? (Round your answer to the nearest tire.)

Answer 1

Answer: The quantity demanded is decreasing at the rate of $\dfrac{1}{6}\ thousands/week$

Step-by-step explanation:

Since we have given that

$p+x^2=225$

Here, p is the price and x is the quantity demanded.

Price per tire is increasing at the rate of $2/week.

So, $\dfrac{dp}{dw}=2$

Differentiating the given equation w.r.t 'w', so we get that

$\dfrac{dp}{dw}+2x\dfrac{dx}{dw}=0\\\\2+2\times 6\dfrac{dx}{dw}=0\\\\2+12\dfrac{dx}{dw}=0\\\\\dfrac{dx}{dw}=\dfrac{-2}{12}=-\dfrac{1}{6}$

Hence, the quantity demanded is decreasing at the rate of $\dfrac{1}{6}\ thousand/week$