The Diet Problem

Problem:

Minimizing the cost of a meal

- Just few choice listed 
- Between 600 and 900 cal. 
- less than 50% of daily sodium 
- at least 30gm of protein 
- at most 40% of calories are from fat
- fractional meal permitted

Hamburger Large Hamburger Chicken Sandwitch Salad with Chicken French Fries
Total(cal) 250 770 630 190 230
Fat(cal) 80 360 145 45 100
Protein(gm) 30 45 15 25 3
Sodium(mg) 480 1170 800 580 160
Cost($) 1.00 3.00 2.50 3.00 1.00

Formulation of LP

Decision Variable

H = Number of unit of Hamburger 
L = Number of unit of Large Hamburger 
C = Number of unit of Chicken Sandwitches 
S = Number of unit of Salad with Chicken
F = Number of unit of French Fries

Minimizing Cost

Minimize: cost = H + 3L + 2.5C + 3S + F

Constraints

Calorie constraints
    250H + 770L + 360C + 190S + 230F >= 600
    250H + 770L + 360C + 190S + 230F <= 600 

Sodium Constraints
    480H + 1170L + 800C + 580S + 160F >= 600

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