Question: Let the linear programming problem (P) be defined as follows: SuchthatMinimiseZ=5x1+2x23x1+x2122x1+x2102x1x215x1,x20 (i) Consider S1,S2 as the surplus variables for the first two constraints respectively and

Let the linear programming problem (P) be defined as follows: SuchthatMinimiseZ=5x1+2x23x1+x2122x1+x2102x1x215x1,x20

Let the linear programming problem (P) be defined as follows: SuchthatMinimiseZ=5x1+2x23x1+x2122x1+x2102x1x215x1,x20 (i) Consider S1,S2 as the surplus variables for the first two constraints respectively and S3 as the slack variable for the third constraint. Find the number of possible bases for (P) and write them all down but do not continue to solve all of them. (ii) Find the solution for the following two basis (x1,S1,S3) and (x1,x2,S1) only and derive their corresponding Z values. Show whether each basis is feasible or infeasible. Solve (P) graphically by showing clearly the feasible region, all the extreme points as well as the optimal point

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