Qusetion: Write the Linear Programming Formulation for the following problem
A high school dietician is planning menus for the upcoming month. A new item will be spaghetti with sauce. The dietician wants each serving to contain at least 10 grams of protein and at least 40 grams of carbohydrate.
Spaghetti contains 5 grams of protein and 32 grams of carbohydrate per cup.
Each cup of sauce contains 4 grams of protein and 5 grams of carbohydrates. For aesthetic reasons, the dietician wants the ratio of spaghetti to sauce to be 4:1
Spaghetti costs $.30 per cup to buy and prepare, Sauce costs $.40 per cup to buy and prepare. The dietician wants to minimize the cost per serving and keep the calories per serving to 330 or less. The sauce contains 100 calories per cup and the spaghetti contains 160 calories per cup.
Formulate a linear programming model for this problem