Model 5: Cereal Blending

The table at the bottom gives a composition of various foods used in making cereals. The other material in each food is fiber, water, etc. The company blends these food materials and makes two kinds of cereals. In the process of blending, 3% of protein, 5% of starch, and 10% of minerals and vitamins are completely lost from the mix. For each 100 kg of foods added in the blend, the blending process adds 5 kg of other material (mainly water and fat).

Cereal type 1 sells for \$1.50/kg. It should contain at least 22% protein, 2% of minerals and vitamins, and at most 30% of starch by weight. Cereal type 2 sells for \$1.00/kg. It should contain at least 30% starch by weight. The company would like to determine the most profitable product mix that meets the requirements described above.

Formulate this problem as an LP.

Percentage Content (by Weight)
Food Protein Starch Minerals,
Vitamins,etc.
Other Material Price
(\$/kg)
Availability
per Day (kg)
1 45 12 4 39 0.68 1500
2 7 38 1 54 0.27 500
3 12 25 2 61 0.31 1000
4 27 40 3 30 0.45 2000