1) The quantities demanded, q1 and q2, of two products depend on their unit prices, p1 and p2, as follows q1 = 135 − 2p1 − p2, q2 = 205 − p1 − 3p2. The total revenue is defined as R = q1p1 + q2p2. A. How should the prices be set to generate the maximum possible revenue? Apply the Second Derivative Test to show that your answer yields the maximum and not the minimum revenue. B. What is the maximum possible revenue and what are the corresponding values of q1 and q2? 2) Find the maximum and minimum values of the function f(x, y, z) = ax + by + cz, where a, b, c are three positive numbers, on the unit sphere x^2 + y^2 + z^2 = 1.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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1) The quantities demanded, q1 and q2, of two products depend on their unit prices, p1 and p2, as follows

q1 = 135 − 2p1 − p2, q2 = 205 − p1 − 3p2.

The total revenue is defined as R = q1p1 + q2p2.

A. How should the prices be set to generate the maximum possible revenue? Apply the Second Derivative Test to show that your answer yields the maximum and not the minimum revenue.

B. What is the maximum possible revenue and what are the corresponding values of q1 and q2?

2) Find the maximum and minimum values of the function f(x, y, z) = ax + by + cz, where a, b, c are three positive numbers, on the unit sphere

x^2 + y^2 + z^2 = 1.

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