a) 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.    (b) 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. (c) 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.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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(a) 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. 

 

(b) 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.

(c) 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.

(d) Maria learns that the wholesaler has a surplus of green beans and is therefore selling the green beans for a

lower price of $0.50 per lb. Using the same iron requirement from part (c) and the new price of green beans, 

determine the amount of potatoes and green beans Maria should purchase each week.

(e) 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).

(f) Will Edson be happy with the solution in part (e)? Why or why not?

(g) An All-State student task force meets during Body Awareness Week and determines that All-State 

University’s nutritional requirements for iron are too lax and that those for vitamin C are too stringent. The task 

force urges the university to adopt a policy that requires each serving of an entrée to contain at least 120 mg of

iron and at least 500 mg of vitamin C. Using potatoes and lima beans as the ingredients for the dish and using

the new nutritional requirements, determine the amount of potatoes and lima beans Maria should purchase 

each week.

Cutting Cafeteria Costs
A cafeteria at All-State University has one special dish it serves like clockwork every Thursday at noon. This supposedly tasty
dish is a casserole that contains sautéed onions, boiled sliced potatoes, green beans, and cream of mushroom soup. 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 cafeteria provides only a limited selection of dishes for Thursday's lunch (namely, the
casserole).
Maria Gonzalez, the cafeteria manager, is looking to cut costs for the coming year, and she believes that one sure way to cut costs is
to buy less expensive and perhaps lower quality ingredients. Because the casserole is a weekly staple of the cafeteria menu, she
concludes that if she can cut costs on the ingredients purchased for the casserole, she can significantly reduce overall cafeteria
operating costs. She therefore decides to invest time in determining how to minimize the costs of the casserole while maintaining
nutritional and taste requirements.
Maria focuses on reducing the costs of the two main ingredients in the casserole, the potatoes and green beans. These two
ingredients are responsible for the greatest costs, nutritional content, and taste of the dish.
Maria buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.40 per pound (lb), and green beans cost
$1.00 per Ib.
All-State University has established nutritional requirements that each main dish of the cafeteria must meet. Specifically, the dish
must contain 180 grams (g) of protein, 80 milligrams (mg) of iron, and 1,050 mg of vitamin C. (There are 454 g in one Ib and
1,000 mg in one g.) For simplicity when planning, Maria assumes that only the potatoes and green beans contribute to the
nutritional content of the casserole.
Because Maria works at a cutting-edge technological university, she has been searching for information on the Internet to find the
nutritional content of potatoes and green beans. Her research yields the following nutritional information about the two ingredients.
Potatoes
Green Beans
Protein
1.5 g per 100 g
5.67 g per 10 ounces
Iron
0.3 mg per 100g 3.402 mg per 10 ounces
Vitamin C 12 mg per 100 g
28.35 mg per 10 ounces
(There are 28.35 g in one ounce.)
Edson Branner, the cafeteria cook who is surprisingly concerned about taste, informs Maria that an edible casserole must Page 62
contain at least a six-to-five ratio in the weight of potatoes to green beans.
Given the number of students who eat in the cafeteria, Maria knows that she must purchase enough potatoes and green beans to
prepare a minimum of 10 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. Maria 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 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.
Transcribed Image Text:Cutting Cafeteria Costs A cafeteria at All-State University has one special dish it serves like clockwork every Thursday at noon. This supposedly tasty dish is a casserole that contains sautéed onions, boiled sliced potatoes, green beans, and cream of mushroom soup. 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 cafeteria provides only a limited selection of dishes for Thursday's lunch (namely, the casserole). Maria Gonzalez, the cafeteria manager, is looking to cut costs for the coming year, and she believes that one sure way to cut costs is to buy less expensive and perhaps lower quality ingredients. Because the casserole is a weekly staple of the cafeteria menu, she concludes that if she can cut costs on the ingredients purchased for the casserole, she can significantly reduce overall cafeteria operating costs. She therefore decides to invest time in determining how to minimize the costs of the casserole while maintaining nutritional and taste requirements. Maria focuses on reducing the costs of the two main ingredients in the casserole, the potatoes and green beans. These two ingredients are responsible for the greatest costs, nutritional content, and taste of the dish. Maria buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.40 per pound (lb), and green beans cost $1.00 per Ib. All-State University has established nutritional requirements that each main dish of the cafeteria must meet. Specifically, the dish must contain 180 grams (g) of protein, 80 milligrams (mg) of iron, and 1,050 mg of vitamin C. (There are 454 g in one Ib and 1,000 mg in one g.) For simplicity when planning, Maria assumes that only the potatoes and green beans contribute to the nutritional content of the casserole. Because Maria works at a cutting-edge technological university, she has been searching for information on the Internet to find the nutritional content of potatoes and green beans. Her research yields the following nutritional information about the two ingredients. Potatoes Green Beans Protein 1.5 g per 100 g 5.67 g per 10 ounces Iron 0.3 mg per 100g 3.402 mg per 10 ounces Vitamin C 12 mg per 100 g 28.35 mg per 10 ounces (There are 28.35 g in one ounce.) Edson Branner, the cafeteria cook who is surprisingly concerned about taste, informs Maria that an edible casserole must Page 62 contain at least a six-to-five ratio in the weight of potatoes to green beans. Given the number of students who eat in the cafeteria, Maria knows that she must purchase enough potatoes and green beans to prepare a minimum of 10 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. Maria 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 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.
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