solve the system of linear equalities graphically on your paper. is the feasible region founded or not? x-2y = 4 what is the corner poilt of the feasible region? 15 hix

nts in Page 348 This theorem simplifies the job of finding an optimum value. First, graph the feasible region and find all corner points. Then test each point in the objective function. Finally, identify the corner point producing the optimum solution. With the theorem, the problem in Example 1 could have been solved by identifying the five corner points of Figure 7.16: (0, 1), (0, 2), (.5, 2.25), (2, 0), and (1, 0). Then, sub- stituting each of these points into the objective function z = 2x + 5y would identify the corner points that produce the maximum and minimum values of z. Corner Point (0, 1) (0, 2) (.5, 2.25) (2,0) (1, 0) 2(0)+ 5(1) = 5 2(0)+ 5(2) = 10 2(.5) + 5(2.25) = 12.25 2(2) + 5(0) = 4 2(1) + 5(0) = 2 Value of z = 2x + 5y 348 ■ (maximum) From these results, the corner point (.5, 2.25) yields the maximum value of 12.25 and the cor- ner point (1, 0) gives the minimum value of 2. These are the same values found earlier. A summary of the steps for solving a linear programming…

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- V:or 1%AT h. N Q3 L-7.pdf Use the simplex method to find the maximum value of : = 2x, - x, + 2r, Objective funetion subject to the constraints s 10 2x, + x2 X + 2r, - 2x, s 20 X + 2x, s 5 where x, 2 0, x, 2 0, and x, 2 0. 1- Design the below table to solution the problem ? C, В.С В.V X, X2 X3 S1 S2 S3 RHS Ratio S1 1 1 10 S2 1 2 -2 20 S3 1 1 Z=EX,*BC, Z-C, 2-Choose the entering variable? Why? 3-Obtained (by Gauss Jordan elimination) the departing variable row? Why? 1. 2.