Consider the linear program Maximise 3 - 7+1 +639 subject to 921 + 712 563 3+1 - 4225 - 12 21.2220 a By multiplying by 1 as appropriate, write this as a primat tinear program in standard form. Hence solve it by using the primal simplex method with tableaux and the Big 'M' Method IL State values of (21.12 ) that give the optimal solution. [Enter just two numbers separated by a comme sin(a) 8 1 Or 00 c State the optimal value of b State the reduced cost of 31 . Provide an interpretation of the reduced cost of 21 In the options below, will derrote the reduced cost of *1 For small increases of the lower bound of the decision vartable 1the optimal value will decrease by per unit increase The relevant coefficient in the final tableau is c Substituting 1 in for the appropriate stack variable, and substituting into formula for the the objective function in the final tableau gives a O difference of G and hence this is the reduced cost The reduced cost is necessarily osince ay is nonbasic in the optimal solution c. Suppose that the objective function is replaced by : = (A + 7)*7 +6:32, where a > 0 Determine the largest value of A for which the optimal solution remains unchanged. i. For greater values of A determine the optimum point (1,2). /Enter just to number separated by a comma 0 1 sin(a) D D c. Suppose that the objective function is replaced by z = (A + 7) 21 +622, where A > 0. i. Determine the largest value of A for which the optimal solution remains unchanged ii. For greater values of A determine the optimum point (31,12) [Enter just two number separated by a commaj a sin(a) xa 12 O ? The optimum value can now be written as a A+ Enter a Enter B