Given this linear programming model, solve the model and then answer the questions that follow. Maximize12x1 + 18x2+ 15x3where x1 = the quantity of product 1 to make etc.Subject to Machine5x1+4x2+3x3≤160minutesLabor4x1+10x2+4x3≤288hoursMaterials2x1+2x2+4x3≤200poundsProduct 2 x2≤16units 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=

Name: Given this linear programming model, solve the model and then answer t
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Description: Given this linear programming model, solve the model and then answer the questions that follow. Maximize12x1 + 18x2+ 15x3where x1 = the quantity of product 1 to make etc.Subject to Machine5x1+4x2+3x3≤160minutesLabor4x1+10x2+4x3≤288hoursMaterials2x

Answered: Given this linear programming model,…

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Chapter6: Linear Systems

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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:

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