Quiz 4 A manufacturer makes and sales four types of products: Product X, Product Y, Product Z,...
Quiz 4
A manufacturer makes and sales four types of products: Product X, Product Y, Product Z, and Product W.
The resources needed to produce one unit of each product and the sales prices are given in the following Table.
|
Resource |
Product X |
Product Y |
Product Z |
Product W |
|
Steel (lbs) |
2 |
3 |
4 |
7 |
|
Hours of Machine Time (hours) |
3 |
4 |
5 |
6 |
|
Sales Price ($) |
4 |
6 |
7 |
8 |
- Currently, 4,600 pounds of steel and 5,000 machine hours are available.
- To meet customer demands, exactly 950 total products must be produced.
- Customers also demand that at least 400 units of Product W be produced.
Formulate an LP that can be used to maximize sales revenue for the manufacturer.
LP Formula
Let Pi be the number of product type i produced by the manufacturer, where i = X, Y, X, and W.
MAXIMIZE 4 PX + 6 PY + 7 PZ + 8 PW
Subject To
2 PX + 3 PY + 4 PZ + 7 PW <= 4600 ! Available Steel
3 PX + 4 PY + 5 PZ + 6 PW <= 5000 ! Available Machine Hours
PX + PY + PZ + PW = 950 ! Total Demand
PW >= 400 ! Product W Demand
PX >=0
PY >=0
PZ >=0
PW >=0
Task 1 (20 points):
Solve the given model using Graphical Solution Method.
Show all your work!
Homework Answers
In this question, there are 4 decision variables PX,PY, PZ and PW.
Here more than 2 decision variables are available hence solution by graphical method is not useful.
The solution of this problem is obtained by simplex method or any other method.
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