products, A and B, and the resources, Q, R, and S, required to produce them. Resource Q R S Profit per unit Resource Usage per Unit Produced Product A Product B 2 1 2 13 3 3 23 3 2 Amount of Resource Available 2 24 2 All the assumptions of linear programming hold. (a) Formulate a linear programming model for this problem. DI (b) Solve this model graphically. (c) Verify the exact value of your optimal solution from part (b) by solving algebraically for the simultaneous solution of the

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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3.2-1. The following table summarizes the key facts about two
products, A and B, and the resources, Q, R, and S, required to
produce them.
Resource
Q
R
S
Profit per unit
Resource Usage
per Unit Produced
Product A Product B
213
2
3
3
123
1
3
2
Amount of Resource
Available
2
224
2
4
All the assumptions of linear programming hold.
(a) Formulate a linear programming model for this problem.
D,I (b) Solve this model graphically.
(c) Verify the exact value of your optimal solution from part (b)
by solving algebraically for the simultaneous solution of the
relevant two equations.
Transcribed Image Text:3.2-1. The following table summarizes the key facts about two products, A and B, and the resources, Q, R, and S, required to produce them. Resource Q R S Profit per unit Resource Usage per Unit Produced Product A Product B 213 2 3 3 123 1 3 2 Amount of Resource Available 2 224 2 4 All the assumptions of linear programming hold. (a) Formulate a linear programming model for this problem. D,I (b) Solve this model graphically. (c) Verify the exact value of your optimal solution from part (b) by solving algebraically for the simultaneous solution of the relevant two equations.
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