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 …show more content…

And found the original context two basic solutions are to reduce costs based solution into peas.

Q 5) Maria decides that she wants to purchase lima beans instead of green beans since lima beans are less expensive and provide a greater amount of protein and iron than green beans. Maria again wields her absolute power and forces Edson to change the recipe to include lima beans instead of green beans. Maria knows she can purchase lima beans for $0.60 per lb from the wholesaler. She also knows that lima beans contain 22.68 g of protein per 10 ounces of lima beans, 6.804 mg of iron per 10 ounces of lima beans, and no vitamin C. Using the new cost and nutritional content of lima beans, determine the amount of potatoes and lima beans Maria should purchase each week to minimize the ingredient costs while meeting nutritional, taste, and demand requirements. The nutritional requirements include the reduced iron requirement from part (c).
Answer:
Lima Beans Lima Beans
Protein 22.68 g per 10 ounces 8 g per 100 g → 8%
Iron 6.804 mg per 10 ounces → 2.4 mg per 100 g → 2.4%
Vitamin C 0 0%

Model becomes as follows:

Putting values in LINDO:
LINDO obtained as follows:

Objective value: 9.843062 Variable Value Reduced Cost P 8750.000 0.000000 G 1614.583 0.000000

Row Slack or Surplus