Nutrifeed, a hog feedlot operation near Houston, Texas blends ingredients to mak

Question

Nutrifeed, a hog feedlot operation near Houston, Texas blends ingredients to make low cost feed for its hogs. Oats and corn are the principal ingredients of the hog feed. The current costs for oats and corn are s 12 cents and 7 cents respectively. Nutrifeed requires a minimum of 3,000 mineral units, 4,000 calories, and 2,000 units of vitamins per day for each hog. Each pound of oats supplies 200 mineral units, 200 calories, and 100 units of vitamins. Each pound of corn supplies 100 mineral units, 300 calories, and 200 units of vitamins. Formulate this problem as a linear programming problem.

Explanation / Answer

Decision Variables -

Oats: X1 units used

Corn: X2 units used

Cost of oats in cents /unit: 12

Cost of Corn in cents /unit: 7

Objective function to minimize the cost of blending –

Min Z = (12 x X1 + 7 x X2)

Constraints:

Minerals        : 200 x X1 +100 x X2 >= 3000

Calories         : 200 x X1 +300 x X2 >= 4000

Vitamins       : 100 x X1 +200 x X2 >= 2000

X1 & X2 > = 0

Solver solution:

Minerals        : 200 x X1 +100 x X2 >= 3000

Calories         : 200 x X1 +300 x X2 >= 4000

Vitamins       : 100 x X1 +200 x X2 >= 2000

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