Advanced: Formulation of an initial tableau and interpretation of final matrix using the Simplex method Hint: Reverse the signs and ignore the entries of 0 and 1. You are not required to solve the model.

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

The manufacturing 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 XI, X2, and X3 respectively); (2 marks)

(c) indicate, with explanations, which will be the ‘entering variable’ and ‘leaving variable’ in the first iteration; (2 marks)

(d) interpret the final matrix of the simplex solu¬ tion 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 of23 per month to be supplied.

Transcribed Image Text:

Chemical constituents: percentage make-up per tonne Nitrate Phosphate X1 X2 X3 2220 10 10 20 1200 Potash Filler 2200 10 10 666 60 60 60