Use the function barnes to Minimize z = 5x1 +7x2 +10x3 subject to x1 + x2 + x3 ≥ 4, x1+2x2+4x3≥5, and x1,x2,x3≥0. Maximize p=4y1+5y2 subject to y1+y2≤5, y1+2y2≤7, y1+4y2≤10, and y1,y2≥0. By introducing slack variables and subtracting one from each equality, write the constraints as equalities. Hence apply the function barnes to solve this problem. Notice that the optimum value of p for this problem is equal to the optimum value of z in Problem 9.1. Problem 9.2 is the dual of Problem 9.1. Thus, the optima of the objective function of Problem 9.1 and its dual, Problem 9.2, should be equal.
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