Lpp Cafetaria Case Solution
QAUNTITATIVE TECHNIQUES
SOLUTION FOR THE CASE
CUTTING CAFETERIA COSTS
LPP MODEL FOR CAFETERIA COST CUTTING
Objective:
To reduce the purchase of potato and green beans, so as to meet the conditions of the various constraints to achieve the goal of minimizing the purchase cost.
Constraint conditions:
Potatoes Green Beans
Protein 1.5 g per 100 g → 1.5% 2 g per 100 g → 2%
Iron 0.3 mg per 100 g → 0.3% 1.2 mg per 100 g → 1.2%
Vitamin C 12 mg per 100 g → 12% 10 mg per 100 g → 10%
Q 1)
Determine the amount of potatoes and green beans Maria should purchase each week for the casserole to minimize the ingredient costs while meeting nutritional, taste, and demand requirements. Before she makes her final decision, Maria plans to explore the following questions independently except where otherwise indicated.
Answer:
1) The decision variables are:
P: The amount of potatoes purchased per week
G: The amount of beans purchased per week
Such that, Objective Function: Subject to constraints:
The first three constraints are nutritional constraints: constraints on protein, iron, and vitamin contents respectively.
Putting these values in LINDO:
Q. 2)
Maria is not very concerned about the taste of the casserole; she is only concerned about meeting nutritional requirements and cutting costs. She therefore forces Edson to change the recipe to allow for only at least a one to two ratio in the weight of potatoes to green beans. Given the new recipe, determine the amount of potatoes and green beans Maria should purchase each week.
Answer:
In this case, the taste constraint is changed.
The new constraint is:
Pounds of potatoes / Pounds of green beans >1/2
So, rebuilding the model as follows:
Object function & constraints: Putting value in LINDO:
LINDO obtained as follows: Objective value: 16.22614 Variable Value Reduced Cost
SOLUTION FOR THE CASE
CUTTING CAFETERIA COSTS
LPP MODEL FOR CAFETERIA COST CUTTING
Objective:
To reduce the purchase of potato and green beans, so as to meet the conditions of the various constraints to achieve the goal of minimizing the purchase cost.
Constraint conditions:
Potatoes Green Beans
Protein 1.5 g per 100 g → 1.5% 2 g per 100 g → 2%
Iron 0.3 mg per 100 g → 0.3% 1.2 mg per 100 g → 1.2%
Vitamin C 12 mg per 100 g → 12% 10 mg per 100 g → 10%
Q 1)
Determine the amount of potatoes and green beans Maria should purchase each week for the casserole to minimize the ingredient costs while meeting nutritional, taste, and demand requirements. Before she makes her final decision, Maria plans to explore the following questions independently except where otherwise indicated.
Answer:
1) The decision variables are:
P: The amount of potatoes purchased per week
G: The amount of beans purchased per week
Such that, Objective Function: Subject to constraints:
The first three constraints are nutritional constraints: constraints on protein, iron, and vitamin contents respectively.
Putting these values in LINDO:
Q. 2)
Maria is not very concerned about the taste of the casserole; she is only concerned about meeting nutritional requirements and cutting costs. She therefore forces Edson to change the recipe to allow for only at least a one to two ratio in the weight of potatoes to green beans. Given the new recipe, determine the amount of potatoes and green beans Maria should purchase each week.
Answer:
In this case, the taste constraint is changed.
The new constraint is:
Pounds of potatoes / Pounds of green beans >1/2
So, rebuilding the model as follows:
Object function & constraints: Putting value in LINDO:
LINDO obtained as follows: Objective value: 16.22614 Variable Value Reduced Cost