A cook is puzzling over the number of pounds of food he should purchase in order to minimize his cost. He has always bought his food from a small health food store in town. The store sells two types of mixtures. Both of these mixtures contain the three ingredients needed, but the cook needs his own special ratio of these ingredients to meet the requirements of a certain diet. The chart below shows that the diet is to be made up of at least 9 grams of Vitamin B-12, at least 30 grams of calcium, and at least 24 grams of iron. As the chart also shows the ratios for each of the three ingredients in the two mixtures the store sells is not the same as what the cook needs. The cook wants to minimize his costs, and have the minimum requirements met once he combines the two mixtures and cooks up the entire blend.
Dietary Constraints
Vitamin B-12
Calcium
Iron
Minimum Requirements
9 grams
30 grams
24 grams
Farmer’s Mixture A
1 gram per pound
6 gram per pound
8 gram per pound
= $3.00 per pound
Farmer’s Mixture B
3 gram per pound
5 gram per pound
3 gram per pound
= $5.00 per pound