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 theextreme point solutions. From this representation find the optimalsolution.
c. Analytically determine all solutions that derive from theintersection of two constraints or nonnegativity restrictions.Identify whether or not these solutions are feasible, and indicatethe corresponding objective function values. Which one isoptimal?
d.Let the slack variables for the first two constraints, x3andx4, be the axes of the graph, and sketch the geometricrepresentation of the model. Show an iso-objective line in thesevariables, and from it determine the optimal solution.
