Suppose that separable programming has been applied to a certain problem (the “original prob-lem”) to convert it to the following equivalent LP model maxz=5x11+4x12+2x13+4x21+x22s. t. 3x11+3x12+3x13+2x21+2x22≤252x11+2x1 2+2x13−x21−x22≤10x11≤2x12≤3x21≤3x22 ≤1x11,x12,x13,x21,x22≥0
1. What was the mathematical model for the original problem? Answer this by plotting the profit graph for each of the original activities and then writing the optimization model (do only the step number 5 of the modeling process) for the original problem in terms of the original decision variables (Hint: Pay special attention to the constraints)(50 points).