Q2: (20pt) Suppose the only foods in the world are as follows: Energy Protein Ca
ID: 366459 • Letter: Q
Question
Q2: (20pt) Suppose the only foods in the world are as follows: Energy Protein Calcuim Price Limit Food Oatmeal Chicken Eggs Whole Milk Serving Size (kcal) g mg) (cents/serving) (servings/d 100g 2 Large 237cc 170g 260g 110 205 160 160 120 260 24 32 13 12 285 20 19 herry Pie Pork&Beans; 80 After consulting with nutritionists, we decree that a satisfactory diet has at least 2000 kcal of energy, 55 g of protein, and 800 mg of calcium (vitamins and iron are supplied by pills). While some of us would be happy to subsist on 10 servings of pork and beans, we have decided to impose variety by having a limit on the number of servings/day for each of our six foods Formulate this problem as an LP model. NO need to solve it.Explanation / Answer
Decision variables:
Let x1 = No of servings of oatmeal per day
x2 = no of servings of chicken per day
x3 = no of servings of eggs per day
x4 = no of servings of Whole milk per day
x5 = no of servings of cherry pie per day
x6 = no of servings of pork and beans per day
Objective function is to minimize cost
Z = min 3x1+ 24x2+ 13x3+ 9x4+ 20x5+ 19x6
Constraints:
110x1+ 205x2+ 160x3+ 160x4+ 420x5+ 260x6>=2000
4x1+ 32x2+ 13x3+ 8x4+ 4x5+ 14x6>=55
2x1+ 12x2+ 54x3+ 285x4+ 22x5+ 80x6>=800
x1<=4
x2<=3
x3<=2
x4<=8
x5<=2
x6<=2
x1,x2,x3,x4,x5,x6>=0
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