TheBatteryParkStablefeedsandhousesthehorsesusedtopulltourist-filledcarriagesthro

Question

TheBatteryParkStablefeedsandhousesthehorsesusedtopulltourist-filledcarriagesthroughthestreetsofCharleston’shistoricwaterfrontarea.Thestableowner,anex-racehorsetrainer,recognizestheneedtosetanutritionaldietforthehorsesinhiscare.Atthesametime,hewouldliketokeeptheoveralldailycostoffeedtoaminimum. Thefeedmixesavailableforthehorses’dietareanoatproduct,ahighlyenrichedgrain,andamineralproduct.Eachofthesemixescontainsacertainamountoffiveingredientsneededdailytokeeptheaveragehorsehealthy.Thetableonthispage showstheseminimumrequirements,unitsofeach ingredientperpoundoffeedmix,andcostsforthe threemixes. Inaddition,thestableownerisawarethatanoverfedhorseisasluggishworker.Consequently,hedeterminesthat6poundsoffeedperdayarethemostthatanyhorseneedstofunctionproperly, and he also wants at least 0.25 LBS of each feed type. Formulatethisproblem as a Linear program. Add a text-box, where you can write your formulation clearly.

Feed Mix Ingredient Requirements Oat Product (Units/LB) Enriched Grain (Units/LB) Mineral (Units/LB) Minimum Daily requirements A 2.2 3 1 5.5 B 0.5 1.1 0.5 2.5 C 3 5 6.3 9 D 0.9 1.5 2 7 E 0.5 0.45 1.5 5 Cost/lb $0.10 $0.15 $0.18

Explanation / Answer

Decision Variable:

Let

X1 be the amount of Oats product in feed mix

X2 be the amount of enriched grain in feed mix

X3 be the amount of mineral in feed mix

Objective Function:

Objective of stable is to keep the overall daily cost of feed to a minimum. The cost function is given as:

Min Z = $0.10X1 + $0.15X2 + $0.18X3

Subject To:

Minimum Requirements of Ingredients in the feed mix.

2.2X1 + 3X2 + X3 5.5                       (Ingredient A minimum requirement)

0.5X1 + 1.1X2 + 0.5X3 2.5             (Ingredient B minimum requirement)

3X1 + 5X2 + 6.3X3 9                        (Ingredient C minimum requirement)

0.9X1 + 1.5X2 + 2X3 7                    (Ingredient D minimum requirement)

0.5X1 + 0.45X2 + 1.5X3 5              (Ingredient E minimum requirement)

Maximum amount of feed require per day is 6 pounds,

X1 + X2 + X3 6

Feed mix should contain at least 0.25 lbs of each feed

X1 0.25

X2 0.25

X3 0.25

(Non-negtivity constraints are not required here, as due to above three constraints)

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