23. Given below is the simplex tableau for a maximisation type of linear programming problem:

Giving reasons in brief, answer the following questions:

(i) Does the tableau represent an optimal solution?
(ii) Are there more than one optimal solution?
(iii) Is this solution degenerate?
(iv) Is this solution feasible?

(v) If S1 is slack in machine A (in hours/week) and S2 in machine B (in hours/week), which of these machines is used to the full capacity when producing according to this solution?
(vi) A customer would like to have one unit of product x1 and is willing to pay in excess of the normal price in order to get it. How much should the price be increased to ensure no reduction in profit?
(vii) How many units of the two products x1 and x2 are being produced according to this solution and what is the total profit?
(viii) Machine A (associated with slack S1, in hours/week) has to be shut down for repairs for 2 hours next week. How much will the reduction in profits be?
(ix) What is the maximum You would be prepared to pay for another hour (per week) of capacity each on machines A and B?
(x) What are the shadow prices of the machine hours?

Transcribed Image Text:

Basis x1 x2 S S b x2 4 1 1 1 0 S 0 0 -1 1 62 3 4 0 0 Cj 4 4 4 0 24 Zj cj-zj -1 4 0