Formulation of LPP - 10 Diet Plam with Minimum Cost

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Ms. HIDIMBA’s diet requires that all the food she eats come from one of the four “basic food groups“. At present, the following four foods are available for consumption: brownies, chocolate ice cream, cola, and pineapple cheesecake. Each brownie costs ` 50 each scoop of chocolate ice cream costs ` 20, each bottle of cola costs ` 30, and each pineapple cheesecake costs ` 80. Each day, she must take at least 500 calories, 6 oz of chocolate, 10 oz of sugar, and 8 oz of fat (oz = ounces). The nutritional content per unit of each food is shown in Table.
Formulate an LP model that can be used to satisfy her daily nutritional requirements at minimum cost.
Calories Chocolate (oz) Sugar (oz) Fat (oz)
Brownie 400 3 2 2
Choco Ice cream
(1 scoop) 200 2 2 4
Cola (1 bottle) 150 0 4 1
Pineapple
Cheese-cake 500 0 4 5

General Mathematical Model of LPP:
The number of problems, showing how to model them by the appropriate choice of decision variables, objective, and constraints. Any linear programming problem involving more than two variables may be expressed as follows:

Find the values of the variable x1, x2,............, xn which maximize (or minimize) the objective function
 Z = c1x1 + c2x2 + .............. + cnxn

 subject to the constraints
a11x1 + a12x2 + ............. + a1nxn ≤ b1
a21x1 + a22x2 + ............. + a2nxn ≤ b2
........................
am1x1 + am2x2 + .............. + amnxn ≤ bm
and meet the non negative restrictions
x1, x2, ..., xn ≥ 0

a) A set of values x1, x2,.. xn which satisfies the constraints of linear programming problem is called its solution.

b) Any solution to a linear programming problem which satisfies the non negativity restrictions of the problem is called its feasible solution.

c) Any feasible solution which maximizes(or minimizes) the objective function of the linear programming problem is called its optimal solution

OR, Operations Management, Math, Statistics, OM, Operations Management, Programming, Formulation, Diet Plan, Nutrition, Chocolate, Cheese Cake, Minimization, Decision Variables, Objective Function, Constraints, LPP, MBA, MCA, CA, CS, CWA, BBA BCA, BCom, MCom, GRE, GMAT, Grade 11, Grade 12, Class 11, Class 12, IAS, CAIIB, FIII, IBPS, BANK PO, UPSC, CPA, CMA

[txlsnzw]

Thanks for your lecture. There's a lot of help that solves many problems in answering LP-model formulation.

[dariuscoetzee]

where can I find the next lesson of this part?

[nithinbittu]

Problem 7. Dietary optimisation
There are six different foods: Bread, Milk, Cheese, Fish, Potato and Yogurt:
Bread Milk Cheese Potato Fish Yogurt
Cost, $ 2.0 3.5 8.0 1.5 11.0 1.0
Protein, g 4.0 8.0 7.0 1.3 8.0 9.2
Fat, g 1.0 5.0 9.0 0.1 7.0 1.0
Carbohydrates, g 15.0 11.7 0.4 22.6 0.0 17.0
Calories, Cal 90 120 106 97 130 180
(1) We have to find a diet that contains not less than 150 calories, not more than 10 g
of protein, not less than 10g of carbohydrates and not less than 8 g of fat. In
addition the diet should include at least 0.5kg of fish and not more than 1 cup of
milk. Find the diet that has minimal cost.
(2) Select 5-7 different foods you usually have, search the related information and
form a similar table as above. Formulate two LP problems (one is to minimise the
cost, the other uses cost as a constraint). After solving each of the two problems,
do a sensitivity analysis on the cost of one or two foods.
Use both MATLAB Optimisation Toolbox and Excel Solver to solve the problems
and perform sensitivity analysis. can you please help me in solving this