A rancher has a minimum weekly nutritional requirements for a horse Protein: 40l

Question

A rancher has a minimum weekly nutritional requirements for a horse

Protein: 40lbs

Carbohydrates: 20lbs

Roughage: 45lbs

These are obtained by the follwing sources:

HAY(per bale): Protein= 0.5, Carb.=2.0, Roughage=5.0 with COST: $1.80

OATS(per sack): Protein=1.0lb, Carb.(lb)=4.0, Roughage(lb)=2.0 with COST: $3.50

HIGH PROTEIN CONC.(per sack): Protein(lb)=6.0, Carb(lb)=1.0, Roughage(lb)=1.00 with COST: $1.00

Requirements per horse (per week): Protein(lb)=40.0, Carb.(lb)=20.0, Roughage(lb)=45.0

Formulate a mathematical model to determine how to meet the minimum nutritional requriements at minimum cost?

Explanation / Answer

Let H= # hay bales, O = # of sacks of oats and P = # sacks of protein concentrate.

we want to mimimize:
cost = 1.8 H + 3.5 O + 1 P

subject to:

40 0.5 H + 1 O + 6 P (protein)

20 2 H + 4 O + 1 P (Carb)

45 5 H + 2 O + 1 P (roughage)

0 O,H,P

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