Question

Given the following linear programming model, answer the questions that follow. You are given the result of a computer program. The results are Maximize 12 X1 + 18 X2 + 15 X3 Subject to: Machine Constraint: 3 X1 + 4 X2 + 3 X3 < 160 Labor Constraint: 6 X1 + 10 X2 + 4 X3 < 288 Materials Constraint: 2 X1 + 2 X2 + 7 X3 < 200 Product 2 Constraint: X1 < 16 1. What is the optimal solution? 2. What is the profit? 3. If the profit of Product 3 was changed to $15.50 and the profit of Product 1 was changed $11.90, would that change the solution? Provide proof.

          Given the
following linear programming model, answer the questions that
follow.  You are given the result of a computer program. 
The results are
Maximize     12 X1 + 18
X2 + 15 X3
Subject
to:
Machine
Constraint:   3 X1 + 4 X2 + 3
X3 < 160
Labor
Constraint:        6 X1 +
10 X2 + 4 X3 < 288
Materials
Constraint:  2 X1 + 2 X2 + 7
X3 < 200
Product 2
Constraint:  X1 < 16
1. What is the optimal solution?
2. What is the
profit?
3. If the profit
of Product 3 was changed to $15.50 and the profit of Product 1 was
changed $11.90, would that change the solution? Provide
proof.

Show more…

Added by Amy W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/15/2023

Step 1

First, we need to find the optimal solution for the given linear programming model. To do this, we can use the simplex method or graphical method. For simplicity, let's use the graphical method. We have the following constraints: $$3X_1 + 4X_2 + 3X_3 \leq Show more…

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Given the following linear programming model, answer the questions that follow. You are given the result of a computer program. The results are Maximize 12 X1 + 18 X2 + 15 X3 Subject to: Machine Constraint: 3 X1 + 4 X2 + 3 X3 < 160 Labor Constraint: 6 X1 + 10 X2 + 4 X3 < 288 Materials Constraint: 2 X1 + 2 X2 + 7 X3 < 200 Product 2 Constraint: X1 < 16 1. What is the optimal solution? 2. What is the profit? 3. If the profit of Product 3 was changed to $15.50 and the profit of Product 1 was changed $11.90, would that change the solution? Provide proof.

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