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Project 31 − the Diet Problem: Ordering Meals from McDonald's

question 30

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Project 3.1 − The Diet Problem: Ordering Meals from McDonald's
Based on: Robert A.Bosch,"Big Mac Attack: The Diet Problem revisited,Eating at McDonald's," OR/MS Today,
August 1993,pp 30-31.
Tina Simpson is a new fourth-grade teacher at Forest Ridge Elementary.The first teacher workshop for the upcoming school year is next Monday and by majority vote,McDonald's was selected as the food of choice.As the new person,Tina is tasked with developing the meal for the workshop.McDonald's has graciously offered to deliver whatever food Tina decides to order,along with a variety of condiments applicable to whatever is ordered.Rather than offer a menu choice,Tina has decided to simply order the same meal for each person in the workshop.
To get started,Tina took a trip to McDonald's and obtained their published information on the nutritional content of their food.That data is summarized in the table below.
Project 3.1 − The Diet Problem: Ordering Meals from McDonald's Based on: Robert A.Bosch, Big Mac Attack: The Diet Problem revisited,Eating at McDonald's, OR/MS Today, August 1993,pp 30-31. Tina Simpson is a new fourth-grade teacher at Forest Ridge Elementary.The first teacher workshop for the upcoming school year is next Monday and by majority vote,McDonald's was selected as the food of choice.As the new person,Tina is tasked with developing the meal for the workshop.McDonald's has graciously offered to deliver whatever food Tina decides to order,along with a variety of condiments applicable to whatever is ordered.Rather than offer a menu choice,Tina has decided to simply order the same meal for each person in the workshop. To get started,Tina took a trip to McDonald's and obtained their published information on the nutritional content of their food.That data is summarized in the table below. Tina wants the meal to be nutritionally complete.The National Research Council publishes their Recommended Daily Allowances.In this publication,they contend that a diet in this case the meal)should provide at least 100 percent of the U.S.RDA of numerous nutrients.The specific amount of the RDA depends on such factors as age,weight and gender.In addition,the council recommends daily sodium and cholesterol intakes be kept to at most 2.4 grams of sodium and 300 milligrams of cholesterol.Further,at most 30 percent of the calories consumed should come from fat,and at most 10 percent from saturated fat.Each gram of fat contains 9 calories. Based on the above information,Tina wants to design a least-cost meal that provides at least 100% of the U.S.RDA of vitamins A,C,B<sub>1</sub>,B<sub>2</sub>,niacin,calcium,and iron;supplies at least 55 grams of protein;contains at most 3 grams of sodium;and contains at most 30 percent of its calories from fat.Only those foods list in the table above are available for the meal. Formulate the LP model for Tina's problem.Develop a spreadsheet model of the problem and use Excel Solver to determine the least-cost meal that meets all the stated requirements. What is the recommended meal? Is this meal reasonable? If not,modify the model to obtain what you believe to be a reasonable meal that meets the stated requirements.
Project 3.1 − The Diet Problem: Ordering Meals from McDonald's Based on: Robert A.Bosch, Big Mac Attack: The Diet Problem revisited,Eating at McDonald's, OR/MS Today, August 1993,pp 30-31. Tina Simpson is a new fourth-grade teacher at Forest Ridge Elementary.The first teacher workshop for the upcoming school year is next Monday and by majority vote,McDonald's was selected as the food of choice.As the new person,Tina is tasked with developing the meal for the workshop.McDonald's has graciously offered to deliver whatever food Tina decides to order,along with a variety of condiments applicable to whatever is ordered.Rather than offer a menu choice,Tina has decided to simply order the same meal for each person in the workshop. To get started,Tina took a trip to McDonald's and obtained their published information on the nutritional content of their food.That data is summarized in the table below. Tina wants the meal to be nutritionally complete.The National Research Council publishes their Recommended Daily Allowances.In this publication,they contend that a diet in this case the meal)should provide at least 100 percent of the U.S.RDA of numerous nutrients.The specific amount of the RDA depends on such factors as age,weight and gender.In addition,the council recommends daily sodium and cholesterol intakes be kept to at most 2.4 grams of sodium and 300 milligrams of cholesterol.Further,at most 30 percent of the calories consumed should come from fat,and at most 10 percent from saturated fat.Each gram of fat contains 9 calories. Based on the above information,Tina wants to design a least-cost meal that provides at least 100% of the U.S.RDA of vitamins A,C,B<sub>1</sub>,B<sub>2</sub>,niacin,calcium,and iron;supplies at least 55 grams of protein;contains at most 3 grams of sodium;and contains at most 30 percent of its calories from fat.Only those foods list in the table above are available for the meal. Formulate the LP model for Tina's problem.Develop a spreadsheet model of the problem and use Excel Solver to determine the least-cost meal that meets all the stated requirements. What is the recommended meal? Is this meal reasonable? If not,modify the model to obtain what you believe to be a reasonable meal that meets the stated requirements.
Tina wants the meal to be nutritionally complete.The National Research Council publishes their Recommended Daily Allowances.In this publication,they contend that a diet in this case the meal)should provide at least 100 percent of the U.S.RDA of numerous nutrients.The specific amount of the RDA depends on such factors as age,weight and gender.In addition,the council recommends daily sodium and cholesterol intakes be kept to at most 2.4 grams of sodium and 300 milligrams of cholesterol.Further,at most 30 percent of the calories consumed should come from fat,and at most 10 percent from saturated fat.Each gram of fat contains 9 calories.
Based on the above information,Tina wants to design a least-cost meal that provides at least 100% of the U.S.RDA of vitamins A,C,B1,B2,niacin,calcium,and iron;supplies at least 55 grams of protein;contains at most 3 grams of sodium;and contains at most 30 percent of its calories from fat.Only those foods list in the table above are available for the meal.
Formulate the LP model for Tina's problem.Develop a spreadsheet model of the problem and use Excel Solver to determine the least-cost meal that meets all the stated requirements.
What is the recommended meal? Is this meal reasonable? If not,modify the model to obtain what you believe to be a reasonable meal that meets the stated requirements.

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