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.