advertisement

MATH 1100: QUANTITATIVE ANALYSIS TEST #3 (VERSION A) Name: This test has 5 pages and 5 problems. No calculators are allowed. You are permitted only a pencil or pen. Work out everything as far as you can before making decimal approximations. 1. Suppose that the demand for a product is given by pq + p = 4. (a) Find the elasticity when p = $2. (b) What type of elasticity is this (unitary, elastic, inelastic)? (c) How would revenue be affected by an increase in price? Date: October 15, 2001. 1 2 MATH 1100: QUANTITATIVE ANALYSIS TEST #3 (VERSION A) 2. Total revenue is R(x) = 18x − x2 where x is the number of units sold. (a) What number of units sold maximizes revenue? (b) What is the maximum revenue? MATH 1100: QUANTITATIVE ANALYSIS TEST #3 (VERSION A) 3 3. (a) Find critical points, values at the critical points, local maxima, local minima and inflection points of 3 C(x) = x3 − x2 − 18x + 6 2 defined for −4 ≤ x ≤ 4. (b) Graph C(x) for −4 ≤ x ≤ 4. 4 MATH 1100: QUANTITATIVE ANALYSIS TEST #3 (VERSION A) 4. Suppose that the number x of units produced per month depends on the number y of thousands of dollars invested with x = 3y + 2y 2 . At what rate will production increase if $10000 is invested and the the investment capital is increasing at a rate of $10 per month? MATH 1100: QUANTITATIVE ANALYSIS 5. Suppose Find dy dx x + exy = y 2 . where x = 0 and y = 1. TEST #3 (VERSION A) 5