Assignment:
Q1. The demand equation for a certain brand of metal alloy audio cassette tape is: 100 x^2 + 9 p^2 = 3600, where x represents the number (in thousands) of ten-packs demanded each week when the unit price is $p. How fast is the quantity demanded increasing when the unit price per ten-pack is $14 and the selling price is dropping at the rate of 15 cents per ten-packs/week? [Hint: To find the value of x when p = 14, solve the equation 100 x^2 + 9 p^2 = 3600 for x when p = 14].
Q2. Suppose the quantity x of Super Titan radial tires made available each week in the marketplace is related to the unit-selling price by the equation: p - (x^2 / 2) = 48, where x is measured in units a thousand and p is in dollars. How fast is the weekly supply of Super Titan radial tires being introduced into the marketplace when x = 6, p = 66, and the price/tire is decreasing at the rate of $3/week?
Q3. The demand function for a certain brand of compact disc is given by the equation: p = - 0.01 x^2 - 0.2 x + 8, where p is the unit price in dollars and x is the quantity demanded each week measured in units of a thousand. Compute the elasticity of demand E(p), and determine whether demand is elastic, inelastic or unitary when x = 15.
Provide complete and step by step solution for the question and show calculations and use formulas.