# (Solved): A dietitian is designing a menu for one person. The daily intakes of meat/fish and vegetables, the c ...

A dietitian is designing a menu for one person. The daily intakes of meat/fish and vegetables, the cost is \$ per 100g, the content per 100g of Protein (>=50g), Fibre (>=25g), Omega-3 (>=0.43g), and Saturated-Fat Content of each item are given in the following order: Cost Prot Fib Om3 Fat Chicken 1.20 25 0 0 3.6 Beef 1.60 5.4 0 0.0246 1.5 Salmon 2.99 19.84 0 2.7 2.2 Lattice 0.6 2.0 3.2 0 0 Carrots 0.53 0.9 0 0 0 Corn 0.85 9 0 2.8 0.7 Derive a linear programming (LP) model to help the dietitian recommend the amount of food for each type. The objective is to minimize the Saturate-Fat intake, while satisfying the protein, Fibre, Omega-3 dietary restrictions given above. In addition, the total cost per meal should not exceed \$7. Let Xi be the amount of food to purchase, i=1,2,...,6 (1- chicken, 2-beef, 3-salmon, 4-lattice, 5-carrots, 6-broccoli. Let Z be the overall Saturate-Fat intake. Identify the optimal values for Xi and Z.

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