Consider the following problem. Maximize z = 8x, +4x+ 6x + 3x + 9x5 s.t. x + 2x + 3x + 3x4 180 4x, + 3x + 2x + x + x 270 x + 3x + x + 3x, 180 (resource 1) (resource 2) (resource 3) x, 0, j = 1, 2, 3, 4, 5 It is known that the basic variables in the optimal solution are X3, X, X5. a) Using this information, please identify the optimal solution (decision variables and the optimal z value) using the formulas for computing the optimal tableau from the initial LP. (i.e. Section 6.2 of the textbook entitled "Some Important Formulas"), b) Find the dual of this LP. c) Determine shadow prices for the three resources using Dual Theorem, d) Let c4 be the coefficient of x4 in the objective function given above. Using the Dual Theorem, please determine, for what values of c will the current basis remain optimal?

Consider the following problem. Maximize z=8x1+4x2+6x3+3x4+9x5s.t.x1+2x2+3x3+3x4180(resource1)4x1+3x2+2x3+x4+x5270(resource2)x1+3x2+x4+3x5180(resource3)xj0,j=1,2,3,4,5 It is known that the basic variables in the optimal solution arex3,x1,x5. a) Using this information, please identify the optimal solution (decision variables and the optimal z value) using the formulas for computing the optimal tableau from the initial LP. (i.e. Section 6.2 of the textbook entitled "Some Important Formulas") b) Find the dual of this c) Determine shadow prices for the three resources using Dual Theorem, d) Let c4 be the coefficient of x4 in the objective function given above. Using the Dual Theorem, please determine, for what values of c4 will the current basis remain optimal? Consider the following problem. Maximize z=8x1+4x2+6x3+3x4+9x5s.t.x1+2x2+3x3+3x4180(resource1)4x1+3x2+2x3+x4+x5270(resource2)x1+3x2+x4+3x5180(resource3)xj0,j=1,2,3,4,5 It is known that the basic variables in the optimal solution arex3,x1,x5. a) Using this information, please identify the optimal solution (decision variables and the optimal z value) using the formulas for computing the optimal tableau from the initial LP. (i.e. Section 6.2 of the textbook entitled "Some Important Formulas") b) Find the dual of this c) Determine shadow prices for the three resources using Dual Theorem, d) Let c4 be the coefficient of x4 in the objective function given above. Using the Dual Theorem, please determine, for what values of c4 will the current basis remain optimal