A cattle rancher in Australia wants to determine a least-cost diet to feed the cattle on his ranch. The diet, however, must contain certain minimum amounts of the following four essential nutrients: fat, carbohydrates, protein, and calcium. These components can be found in three types of cattle food, A, B, and C. The amount of every nutrient in ounces per pound of these cattle foods is shown in the following table:

The cattle daily diet must be a mixture of at least 400 ounces of fat, 600 ounces of carbohydrates, 2,000 ounces of protein, and 1,600 ounces of calcium.

1. Formulate this problem as a linear programming problem.

2. Solve this problem using Excel Solver, and provide the optimal solution values of all variables.

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Nutrients in Ounces per Pound Fat Protein Carbohydrates 150 200 Calcium Cost per Pound $3.00 $5.00 Cattle Food 300 150 150 100 100 200 200 100 300 150 $4.00