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.
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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)
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3. (a) Find critical points, values at the critical points, local maxima, local
minima and inflection points of
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C(x) = x3 − x2 − 18x + 6
2
defined for −4 ≤ x ≤ 4.
(b) Graph C(x) for −4 ≤ x ≤ 4.
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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)
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