Bonus Question 4 ( A firm makes three products, in quantities X, Y and Z. It wishes to maximize its profit function: x-8X+ 16Y+4Z-0.8X2-0.8Y2-2² i) However, in order to satisfy customer orders, it must produce a total of 24 items which are either product X or product Y. Show how many of each of its three products it should produce and find the profit it makes.

Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter14: Firms In Competitive Markets
Section: Chapter Questions
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Bonus Question 4 1
A firm makes three products, in quantities X, Y and Z. It wishes to maximize its profit function:
x=8X+16Y+4Z-0.8X2-0.8Y2-2²
i) However, in order to satisfy customer orders, it must produce a total of 24 items
which are either product X or product Y. Show how many of each of its three
products it should produce and find the profit it makes.
Transcribed Image Text:Bonus Question 4 1 A firm makes three products, in quantities X, Y and Z. It wishes to maximize its profit function: x=8X+16Y+4Z-0.8X2-0.8Y2-2² i) However, in order to satisfy customer orders, it must produce a total of 24 items which are either product X or product Y. Show how many of each of its three products it should produce and find the profit it makes.
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