Question

Druz milling produces three special brand of millet namely
Triple Refined, Double Refined and Regular Refined millet. Producing each of these
three types of brands requires sorting, grinding, packaging and labelling. To produce the
Triple Refined millet requires 2 hour of sorting, 1 hour of grinding, 3 hours of
packaging and 4 hours of labelling. To produce the Double Refined millet requires 1
hour of sorting, 1 hour of grinding, 4 hours of packaging and 3 hours of labelling. To produce
the Regular Refined millet requires 2 hour of sorting, 1 hour of grinding, 2 hours of
packaging and 2 hours of labelling. The total number of hours per week for sorting, grinding,
packaging and labelling is 98, 60, 145 and 160, respectively. In addition, the profit-
contributions is £84 from the Triple Refined brand, £72 from the Double Refined brand and
£52 from the Regular Refined brand.
a. Formulate a linear programming problem for the milling company [3 Marks].
b. Solve the linear programming problem you have formulated using the Simplex
method [9 Marks].
c. Are all the resources are fully utilized? Prove your answer [3 Marks].

Answer 1