Question

You are the manager of a 40 head broodmare farm. The mare’s average weight is 1,000 lbs. ➢ You know the mares in early lactation require: 28.3 Mcal DE, 3 lbs Crude protein, 50 g Ca, 34 g P. ➢ You go to the local feed store and purchase a feed that sells of $8.50/50 lb bag. ➢ The nutrient make up of the feed is: 13.5% CP, 0.5% Ca, and 0.44% P. By the fiber content you estimate the DE to be around 1.3 Mcal/lb. ➢ You feed 1% bwt in grass hay (7% CP, 0.8 Mcal DE/lb, 0.4% Ca, 0.2% P) A. How much of the commercial feed must you feed to meet the mares’ requirements (per head, per day)? 21.76 B. If the hay costs $40/ton, what is the monthly cost to feed these 40 mares, in early lactation (grain cost is given above)? a. Hay b. Grain c. Total

Answer 1

Hi,

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(A)

This question can be solved using linear programming.

Minimum Feeding requirements of Mares:

Crude protein (CP)

Digestible Energy

Calcium

Phosphorous

Nutrients in GRAIN/COMMERCIAL FEED(In 1 lbs):

Crude protein (CP)

Digestible Energy

Calcium

Phosphorous

Cost for 1 lbs

Nutrients in HAY (In 1 lbs):

Crude protein (CP)

Digestible Energy

Calcium

Phosphorous

Cost for 1 lbs

Let's Tabulate all the data given,

Let the mixture of feed contains 'x' lbs of Grain/commercial feed and '100 y' lbs of Hay. (Note: The reason why I chose 100y is that, The mixture of feeding is 1% by weight)

Resources	FOOD 1 GRAIN (x)	FOOD 2 HAY (100 y)	REQUIREMENT
Crude protein (CP) (lbs)
Digestible Energy (Mcal/lbs)
Calcium (g/lbs)
Phosphorous (glbs)
COST ($/lbs)			????

Then we have the constraints,

Total cost Z of purchasing lbs of Grains and lbs of Hay for one mare for one day is given by,

Hence, the mathematical formulation of the problem is,

Minimise

Subject to the constraints,

Solving this graphically we get,Total cost of purchasing lbs of Grains and lbs of Hay for one mare for one day is given by,

Total cost for feeding 40 mares is given by,

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