Question: Can someone help me set up MATLAB linear program?? Problem is below Veronica the owner of Very Veggie Vegeria is creating a new healthy salad
Can someone help me set up MATLAB linear program?? Problem is below
Veronica the owner of Very Veggie Vegeria is creating a new healthy salad that is low in calories but meets certain nutritional requirements. A salad is any combination of the following ingredients: Tomato, Lettuce, Spinach, Carrot, Smoked Tofu, Sunflower Seeds, Chickpeas, Oil.
Each salad must contain: At least 15 grams of protein At least 2 and at most 8 grams of fat At least 4 grams of carbohydrates At most 200 milligrams of sodium At least 40% leafy greens (lettuce and spinach) by mass.
Determine the combination of ingredients that minimizes calories but meets all nutritional requirements. i. Formulate the problem as a linear program with an objective function and all constraints. ii. Determine the optimal solution for the linear program using any software you want. Include a copy of the code/file in the report. iii. What is the cost of the low calorie salad?
My objective function is Minimize c1*21 + c2*16 + c3*40 + c4*41 + c5*585 + c6*120 + c7*164 + c8*884 Constraints are Nutritional Constraints (what each salad must have):
Protein: c1*0.85 + c2*1.62 + c3*2.86 + c4*0.93 + c5*23.4 + c6*16 + c7*9 + c8*0 >= 15
Fat: c1*0.33 + c2*0.20 + c3*0.39 + c4*0.24 + c5*48.7 + c6*5 + c7*2.6 + c8*100 >= 2
Fat: c1*0.33 + c2*0.20 + c3*0.39 + c4*0.24 + c5*48.7 + c6*5 + c7*2.6 + c8*100
Carbs: c1*4.64 + c2*2.37 + c3*3.63 + c4*9.58 + c5*15 + c6*3 + c7*27 + c8*0 >= 4
Sodium: c1*.009 + c2*.028 + c3*.065 + c4*.069 + c5*.0038 + c6*.120 + c7*.078 + c8*0
Leafy greens: 0.4a - 0.6b - 0.6c - 0.6d + 0.4e + 0.4f + 0.4 g + 0.4h
ci >= 0 Not sure if my constraints are correct, do I need to negate them or something??
this is as far as I got for setting up Matlab
Calories
f = [21,16,40,41,585,120,164,884]
The nutritional contents of these ingredients (per 100 grams) and cost are Ingredient Protein Sodium Cost Energy (cal) Fat Carbohydrate (grams) (grams) (grams) (mg) (100g) Tomato 21 0.85 0.33 4.64 9.00 $1.00 Lettuce 16 1.62 0.20 2.37 28.00 $0.75 Spinach 40 2.86 0.39 3.63 65.00 $0.50 Carrot 41 0.93 0.24 9.58 69.00 $0.50 Sunflower Seeds 585 23.4 48.7 15.00 3.80 $0.45 Smoked Tofu 120 16.00 5.00 3.00 120.00 $2.15 Chickpeas 164 9.00 2.6 27.0 78.00 $0.95 Oil 884 0 100.00 0 0 $2.00
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