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Given this linear programming model, solve the model and then answer the questions that follow.   Maximize 12x1 + 18x2+ 15x3 where x1 = the quantity of product 1 to make etc. Subject to        Machine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hours Materials 2x1 + 2x2 + 4x3 ≤ 200 pounds Product 2          x2 ≤ 16 units       x1, x2, x3 ≥ 0   If profit per unit on each product increased by $1, would the optimal values of the decision variables change? What would be the new value of the objective function? The objective function value Z=

Given this linear programming model, solve the model and then answer the questions that follow.   Maximize 12x1 + 18x2+ 15x3 where x1 = the quantity of product 1 to make etc. Subject to        Machine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hours Materials 2x1 + 2x2 + 4x3 ≤ 200 pounds Product 2          x2 ≤ 16 units       x1, x2, x3 ≥ 0   If profit per unit on each product increased by $1, would the optimal values of the decision variables change? What would be the new value of the objective function? The objective function value Z=

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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Given this linear programming model, solve the model and then answer the questions that follow.
 

Maximize 12x1 + 18x2+ 15x3 where x1 = the quantity of product 1 to make etc.
Subject to    

  

Machine 5x1 + 4x2 + 3x3 ≤ 160 minutes
Labor 4x1 + 10x2 + 4x3 ≤ 288 hours
Materials 2x1 + 2x2 + 4x3 ≤ 200 pounds
Product 2          x2 ≤ 16 units
      x1, x2, x3 ≥ 0  

If profit per unit on each product increased by $1, would the optimal values of the decision variables change?
What would be the new value of the objective function?

The objective function value Z=

Expert Solution
Step 1

If the profit of each product is increased by $1 the effect on the decision variables and objective function has to be examined.

The range of optimality is the range by which the coefficients of the objective function can change without affecting the optimality of the solution. This is also given by the Sensitivity Report  by the solver which is as follows:

Variable Cells

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