Quiz 4
A manufacturer makes and sales four types ofproducts: Product X, Product Y, Product Z, and ProductW.
The resources needed to produce one unit of each product and thesales 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 areavailable.
- To meet customer demands, exactly 950 total products must beproduced.
- Customers also demand that at least 400 units of Product W beproduced.
Formulate an LP that can be used to maximize sales revenue forthe manufacturer.
LP Formula
Let Pi be the number of product type i produced by themanufacturer, 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
Suppose manufacturer raises the price of Product Y by 50¢ perunit. What is the new optimal solution to the LP?
Objective Function Value: | |
PX: | |
PY: | |
PZ: | |
PW: | |
