Case study: Reducing cafe costs

A cafe at the university has one special dish it serves like clockwork every Monday at

noon. This supposedly tasty dish is a casserole that contains sauted onions, boiled sliced

potatoes, green beans, and creamof mushroomsoup. Unfortunately, students fail to see

the special quality of this dish, and they loathingly refer to it as the Killer Casserole. The

students reluctantly eat the casserole, however, because the cafe provides only a limited

selection of dishes for Monday's lunch (namely, the casserole).

Jane Lim, the cafe manager, is looking to cut costs for the coming year, and she believes

that one sureway to cut costs is to buy less expensiveandperhaps lower quality

ingredients. Because the casserole is a weekly staple of the cafe menu, she concludes that

if she can cut costs on the ingredients purchased for the casserole, she can significantly

reduce overall cafe operating costs. She therefore decides to invest time in determining

howto minimise the costs of the casserole whilemaintaining nutritional and taste

requirements.

Jane focuses onreducing the costs of the twomain ingredients in the casserole, the

potatoes and green beans. These twoingredients are responsible for the greatest costs,

nutritional content, and taste of the dish.

Jane buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.30

per pound(lb), and green beans cost $0.95 per lb.

Theuniversity has established nutritional requirements that each main dish of the cafe

mustmeet. Specifically, the dish must contain 160 grams (g) of protein, 65 milligrams

(mg)of iron, and 1,000 mg of vitamin C. For simplicity when planning, Jane assumes that

only the potatoes and green beans contribute to the nutritional content of the casserole.

Because Jane works at acutting-edge technological university, she has been exposed to

thenumerous resourceson the Internet. She decides to find the nutritional content of

potatoes and greenbeans.Her research yieldsthe following nutritional information

about the two ingredients.

NutrientPotatoesGreen Beans

Protein1.4 g / 100g5.9 g / 10 oz

Iron0.255 mg / 100 g3.56 mg / 10 oz

VitaminC11 mg/ 100 g29.75 mg / 10 oz

(There are 28.35 g in one ounce, and 16 ounces in one pound)

Eddy Brooks, the cafe cook who is surprisingly concerned about taste, informs Jane that

an edible casserole must contain at least a six-to-five ratio in the weight of potatoes to

green beans.

Given the numberof studentswho eat in the cafe, Jane knows that she must purchase

enough potatoes and green beans for a minimumof 12 kilograms (kg) of casserole

each week. (There are 1,000 g in one kg.) Again, for simplicity in planning, she assumes

that only the potatoes and green beans determine the amount of casserole that can be

prepared. Jane does not establish an upper limit on the amount of casserole to prepare

since she knows all leftovers can be served for many days thereafter or can be used

creatively in preparing other dishes.

a. Determine the amountof potatoes and green beans Jane should purchase each

weekfor the casserole to minimise the ingredient costs while meeting nutritional,

taste, and demand requirements.

Before shemakes her final decision, Jane plans to explore the following questions

independently, except where otherwise indicated.

b. Student Unionmeets during Health Awareness Weekand determines that The

university's nutritional requirements for iron are too lax and that those for

vitamin C are too stringent. The Union urges the university to adopt a policy that

requires each serving of an entre to contain at least 100 mg of iron and at least

500mg of vitamin C. Using the new nutritional requirements, determine the

amountof potatoes and green beans Jane should purchase each week.

c. Jane learns that the wholesaler has a shortage of green beans and is now selling

the green beans for a higher price of $1.20 per lb. Using the new price of the green

beans, determine the amount of potatoes and green beans Jane should purchase

each week.

d. Using the new nutritional requirements in part b and the new price of green beans

in part c, determine the amount of potatoes and green beans Jane should purchase

each week.

e. Based on part d, which required nutrition would affect the cost if it were to be

changed. Why?

Note:Unit of Measurementfor AllResults Should beReportedin ige.

Note:

Students are required to

odevelop a LINEAR/INTEGERPROGRAMMINGmodelto solve the problem.

oanswerto the case questions based on the output of your analysis.

Students are required to submit

oaWord file to explain your mathematical models, to report your answers,

and to write recommendationsfor decision makersbased on the solutions,

and

oan Excel file to demonstrate how youuse Solver to identify the solutions.

You mustensure that the file is in a workable condition before the

submission.