15. A chemical manufacturer is developing three fertiliser compounds for the agricultural industry. The product codes for these products are X1, X2 and X3 and the relevant information is summarised below:

The fertilisers will be sold in bulk and managers have proposed the following prices per tonne:
X1 : Rs 83; X2 : Rs 81; andX3 : Rs 81 The manufacturing costs of each type of fertiliser, excluding materials, are Rs 11 per tonne.
You are required to:

(a) formulate the above data into a linear programming model so that the company may maximise contribution;

(b) construct the initial tableau and state what is meant by 'slack variables' (define X4, X5, X6 as the slack variables for X1, X2, andX3, respectively);

(c) indicate, with explanations, which will be the 'entering variable' and 'leaving variable' in the first iteration; (You are not required to solve the model.)

(d) interpret the final matrix of the simplex solution given below:

(

e) use the final matrix above to investigate:
(i) the effect of an increase in nitrate of 100 tonnes per month;
(ii) the effect of a minimum contract from an influential customer for 200 tonnes of X3 per month to be supplied.

Transcribed Image Text:

X3 *** Chemical constituents: percentage make-up per tonne Nitrate 10 10 20 Phosphate Potash Filler 222 10 20 60 20 10 60 10 10 60 Input prices per tonne Maximum available input in tonnes per month Nitrate Phosphate Rs 150 Rs 60 Potash Rs 120 Filler Rs 10 1,200 2,000 2,200 No limit