The simplex tableau for a maximisation problem of linear programming is given as follows:

Answer the following questions, giving reasons in brief:

(a) Is this solution optimal?

(b) Are there more than one optimal solutions?

(c) Is this solution degenerate?

(d) Is this solution feasible?

(e) If S1 is slack in machine A (in hours/week) and S2 is slack in machine B (in hours/week), which of these machines is being used to the full capacity when producing according to this solution?

(f) 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 in order to ensure no reduction of profits?
(g) How many units of the two products x1 and x2 are being produced according to this solution and what is the total profit?
(h) Machine A (associated with slack S1, in hours/week) has to be shut down for repairs for 2 hours next week. What will be the effect on profits?
(i) How much would you be prepared to pay for another hour (per week) of capacity each on machine A and machine B?

G) A new product is proposed to be introduced which would require processing time of 1/2 hour on machine A and 20 minutes on machine 8. It would yield a profit of Rs 3 per unit. Do you think it is advisable to introduce this product?
The given simplex tableau is reproduced in Table 4.21.

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Product Mix 550 xj X2 S 4 Cj 5 Zj -1 X2 S S Quantity (b;) 1 0 550 -1 0 5 0 5 0 10 3 50 50