# Lpp Cafetaria Case Solution

Topics: Optimization, Nutrition, Vitamin C Pages: 6 (1370 words) Published: September 14, 2010
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:

PotatoesGreen Beans
Protein1.5 g per 100 g → 1.5%2 g per 100 g → 2%
Iron0.3 mg per 100 g → 0.3%1.2 mg per 100 g → 1.2%
Vitamin C12 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 P 4666.667 0.000000 G 5500.000 0.000000

Row Slack or Surplus Dual Price 1 16.22614 -1.000000 2 0.000000 -0.3303965E-01 3 0.000000 -0.1284875 4 60.00000 0.000000 5 3833.333 0.000000 6 166.6667 0.000000 Conclusion:

The original base solution is to change the weight ratio of edible after the base solution into, just to meet the minimum requirement of protein with iron, can be seen from the figure. Protein 180g, 80mg iron and vitamin C1050mg constraints, plus edible and the weight ratio of 1:2 minimum weekly requirements under the 10kg limit, Maria decided to buy 4666.667 g of potatoes with 5500 g of green beans, the required to spend at \$ 16.22614.

Q.3) Maria decides to lower the iron requirement to 65 mg since she determines that the other ingredients, such as the onions and cream of mushroom soup, also provide iron. Determine the amount of potatoes and green beans Maria should purchase each week given this new iron requirement. Answer:

Model Becomes as follows:

LINDO obtained as follows:
Objective value: 14.29883
Variable Value Reduced Cost P 7166.667 0.000000 G 3625.000 0.000000

Row Slack or Surplus Dual Price 1 14.29883 -1.000000 2 0.000000 -0.3303965E-01 3 0.000000 -0.1284875...