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In: Advanced Math

Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 –...

Consider the following linear program. Maximize z= 5x1+ 3x2

subject to 3x1+ 5x2≤15

5x1+ 2x2≤10

– x1+ x2≤2

x2≤2.5

x1≥0, x2≥0

a. Show the equality form of the model.

b. Sketch the graph of the feasible region and identify the extreme point solutions. From this representation find the optimal solution.

c. Analytically determine all solutions that derive from the intersection of two constraints or nonnegativity restrictions. Identify whether or not these solutions are feasible, and indicate the corresponding objective function values. Which one is optimal?

d.Let the slack variables for the first two constraints, x3and x4, be the axes of the graph, and sketch the geometric representation of the model. Show an iso-objective line in these variables, and from it determine the optimal solution.

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