Given the number of students who eat in the cafeteria, Maria knows that she must purchase enough potatoes and green beans to prepare aminimum of 10 kilograms (kg) of casserole each week. (There are 1,000 g in oue kg) Again, for simplicity in planning, she assumes that only the putatues 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. 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 only for 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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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, fur simplicity in planning, slhe assumes that uıly 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.
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 only for 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 prowide 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 Ib. 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 Ib
from the wholesaler. She also knows that lima beans contain 22.68 g of protein and 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
why not?
g. An All-State student task force meets during Body Aware ness 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, deter mine the amount of potatoes and lima beans Maria should purchase
each week.
Transcribed Image Text: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, fur simplicity in planning, slhe assumes that uıly 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. 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 only for 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 prowide 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 Ib. 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 Ib from the wholesaler. She also knows that lima beans contain 22.68 g of protein and 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 why not? g. An All-State student task force meets during Body Aware ness 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, deter mine 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 (Ib).
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 exposed to the numerous
resources on the World Wide Web. She decides to surf the Web to find the nutritional content of potatoes
and green beans. Her research yields the following nutritional information about the two ingredients.
Potatoes
Green Beans
15 g per 100 g
0.3 mg per 100 g
12 mg per 100 g
Protein
5.67 g per 10 ounces
3.402 mg per 10 ounces
28.35 mg per 10 ounces
Iron
Vitamin C
(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 contain at least a six-to-five ratio in the weight of potatoes to green beans.
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 (Ib). 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 exposed to the numerous resources on the World Wide Web. She decides to surf the Web to find the nutritional content of potatoes and green beans. Her research yields the following nutritional information about the two ingredients. Potatoes Green Beans 15 g per 100 g 0.3 mg per 100 g 12 mg per 100 g Protein 5.67 g per 10 ounces 3.402 mg per 10 ounces 28.35 mg per 10 ounces Iron Vitamin C (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 contain at least a six-to-five ratio in the weight of potatoes to green beans.
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