Advanced: Formulation of initial matrix and interpretation of final matrix using the Simple method Hint: Reverse the signs and ignore the entries of 0 and 1.

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

The fertilizers will be sold in bulk and managers have proposed the following prices per tonne

The manufactunng costs of each type of fertilizer, excluding materials, are £11 per tonne.
You are required to:

(a) formulate the above data into a linear programming model so that the company may maximize contribution; (4 marks)

(b) construct the initial Simplex tableau and state what is meant by 'slack variables' (Define X4, X5, X6 as the slack variables for X1 , X2, and X3 respectively); (2 marks)

(c) indicate, with explanations, wh1ch will be the ·entering variable' and 'leaving variable' in the first iteration;
(2 marks)
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:

X1 X2 X3 Chemical constituents: percentage make-up per tonne Nitrate 1220 Phosphate 10 200 10 Input prices per tonne Potash Filler 20 60 110 10 60 10 60 Nitrate 150 Phosphate 60 Potash 120 Filler 10 Maximum available input in tonnes per month Nitrate Phosphate Potash Filler 1200 2000 2200 No limit