The natural diet of a certain animal consists of three foods: A. B. and C. The number of units of calcium, iron, and protein in 1 gram of each food and the average daily intake are given in the table. A scientist wants to investigate the effect of increasing the protein in the animal's diet while not allowing the units of calcium and iron to exceed its average daily intakes. How many grams of each food should be used to maximize the amount of protein in the diet? What is the maximum amount of protein? Units per Gram Food A Food B Food C Intake (units) Average Daily Calcium 24 Iron 16 Protein 4 66 Let x1, X2, and x3 be the grams of food A, food B, and food C in the diet, respectively. Construct a mathematical model in the form of a linear programming problem. Maximize Subject to Calcium constraint Iron constraint X1. X2, Xg 2 0

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