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.
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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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