ABSTRACT
Due to a limited budget you would like to find the most economical mix of food items subject to providing sufficient daily nutrition. The available food items are peanut butter, bananas, and chocolate, and the cost per serving is 20 cents, 10 cents, and 15 cents, respectively. The amount of nutrients of fat, carbohydrates, and protein per serving of peanut butter is 130 grams, 51.6 grams, and 64.7 grams. For bananas, the amounts of these nutrients per serving are 1 gram, 51 grams, and 2 grams, whereas for chocolate the amounts per serving are 12 grams, 22 grams, and 2 grams. Suppose it is decided by a dietician that you need at least 35 grams of fat, at least 130 grams of carbohydrate, and at least 76 grams of protein daily. Then, a combination of these three food items should provide you with sufficient amounts of each nutrient for the day. The problem of determining the least cost combination of the food items that provide a sufficient amount of nutrients can be represented as a problem of the following form:
food items must provide enough fat
food items provide must enough carbohydrates food items provide must enough protein
the problem reveals two major components, i.e., (1) there (minimize cost of food items used) and (2) a set of represent the requirements for the problem (food items must nutrition). A linear programming problem will exhibit the with mathematical representations of the components of the a linear program will consist of decision variables, an set of constraints.
