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Problem 1 Dr. Song will go to McDonald's for dinner tonight. After studying operations research, he feels that he should at least be "smart" enough to figure out the way he eats it. Let's build a model to determine what to eat at McDonald's. QP AD BM FF MC FR SM 1M OJ Required Cost 3.79 4.49 3.99 3.79 1.29 1.79 1.19 1.00 1.89 Prot 28 24 25 14 31 3 15 9. 1 55 VitA 15 15 6. 4 10 100 VitC 10 2 15 15 4 120 100 Calc 30 20 25 15 15 20 30 100 Iron 20 20 20 10 8 15 2 100 Cals 510 370 500 370 400 220 345 110 80 2000 Carb 34 33 42 38 42 26 27 12 20 350 The tables gives the menu (Quarter Pounder, Angus Deluxe, etc.) along with their unit cost (in $) and amount of nutrients contained (Protain, Vitamin A, etc.) The last column of the table gives the daily required amount of nutrients suggested by Dr. Song's doctor. Suppose Dr. Song aims to minimize the cost of his dinner, while he wants to satisfy all the nutrient requirements. Formulate this problem as a linear programming model, and solve it in Excel or Python. In addition to a linear programming model with clear definition of decision variables, objective function, and constraints, you will also be submitting the Excel file (hwk2.xlsx) or the Jupyter notebook file (hwk2.ipynb) on Canvas. Note: It is always a good idea to write down a linear program on a piece of paper before starting coding or doing Excel.

Problem 1 Dr. Song will go to McDonald's for dinner tonight. After studying operations research, he feels that he should at least be "smart" enough to figure out the way he eats it. Let's build a model to determine what to eat at McDonald's. QP AD BM FF MC FR SM 1M OJ Required Cost 3.79 4.49 3.99 3.79 1.29 1.79 1.19 1.00 1.89 Prot 28 24 25 14 31 3 15 9. 1 55 VitA 15 15 6. 4 10 100 VitC 10 2 15 15 4 120 100 Calc 30 20 25 15 15 20 30 100 Iron 20 20 20 10 8 15 2 100 Cals 510 370 500 370 400 220 345 110 80 2000 Carb 34 33 42 38 42 26 27 12 20 350 The tables gives the menu (Quarter Pounder, Angus Deluxe, etc.) along with their unit cost (in $) and amount of nutrients contained (Protain, Vitamin A, etc.) The last column of the table gives the daily required amount of nutrients suggested by Dr. Song's doctor. Suppose Dr. Song aims to minimize the cost of his dinner, while he wants to satisfy all the nutrient requirements. Formulate this problem as a linear programming model, and solve it in Excel or Python. In addition to a linear programming model with clear definition of decision variables, objective function, and constraints, you will also be submitting the Excel file (hwk2.xlsx) or the Jupyter notebook file (hwk2.ipynb) on Canvas. Note: It is always a good idea to write down a linear program on a piece of paper before starting coding or doing Excel.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Problem 1 Dr. Song will go to McDonald's for dinner tonight. After studying operations research, he feels that he should at least be "smart" enough to figure out the way he eats it. Let's build a model to determine what to eat at McDonald's. QP AD BM FF MC FR SM 1M OJ Required Cost 3.79 4.49 3.99 3.79 1.29 1.79 1.19 1.00 1.89 Prot 28 24 25 14 31 3 15 1 55 VitA 15 15 6 8 4 10 2 100 VitC 10 2 15 15 4 120 100 Calc 30 20 25 15 15 20 30 2 100 Iron 20 20 20 10 8 15 100 Cals 510 370 500 370 400 220 345 110 80 2000 Carb 34 33 42 38 42 26 27 12 20 350 The tables gives the menu (Quarter Pounder, Angus Deluxe, etc.) along with their unit cost (in $) and amount of nutrients contained (Protain, Vitamin A, etc.) The last column of the table gives the daily required amount of nutrients suggested by Dr. Song's doctor. Suppose Dr. Song aims to minimize the cost of his dinner, while he wants to satisfy all the nutrient requirements. Formulate this problem as a linear programming model, and solve it in Excel or Python. In addition to a linear programming model with clear definition of decision variables, objective function, and constraints, you will also be submitting the Excel file (hwk2.xlsx) or the Jupyter notebook file (hwk2.ipynb) on Canvas. Note: It is always a good idea to write down a linear program on a piece of paper before starting coding or doing Excel. Problem 2 Central Critical Chemical (CCC) manufactures three chemicals: A, B and C. These chemicals are produced via two production processes: 1 and 2. • Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C. • Running process 2 for an hour costs $1 and yields 2 units of A and 1 unit of B. To meet customer demand, at least 6 units of A, 3 units of B, and 1 unit of C must be produced daily. Suppose you are asked to formulate an LP model for CCC to determine an optimal daily production plan (i.e., how many hours should CCC run process 1 and how many hours should CCC run process 2 each day) that minimizes the total cost. (a) Write down LP model and clearly define the decision variables, the objective function, and constraints. (b) Solve the LP model using the graphical method. (c) Provide a justification on why the divisibility assumption holds for the problem.
Transcribed Image Text:Problem 1 Dr. Song will go to McDonald's for dinner tonight. After studying operations research, he feels that he should at least be "smart" enough to figure out the way he eats it. Let's build a model to determine what to eat at McDonald's. QP AD BM FF MC FR SM 1M OJ Required Cost 3.79 4.49 3.99 3.79 1.29 1.79 1.19 1.00 1.89 Prot 28 24 25 14 31 3 15 1 55 VitA 15 15 6 8 4 10 2 100 VitC 10 2 15 15 4 120 100 Calc 30 20 25 15 15 20 30 2 100 Iron 20 20 20 10 8 15 100 Cals 510 370 500 370 400 220 345 110 80 2000 Carb 34 33 42 38 42 26 27 12 20 350 The tables gives the menu (Quarter Pounder, Angus Deluxe, etc.) along with their unit cost (in $) and amount of nutrients contained (Protain, Vitamin A, etc.) The last column of the table gives the daily required amount of nutrients suggested by Dr. Song's doctor. Suppose Dr. Song aims to minimize the cost of his dinner, while he wants to satisfy all the nutrient requirements. Formulate this problem as a linear programming model, and solve it in Excel or Python. In addition to a linear programming model with clear definition of decision variables, objective function, and constraints, you will also be submitting the Excel file (hwk2.xlsx) or the Jupyter notebook file (hwk2.ipynb) on Canvas. Note: It is always a good idea to write down a linear program on a piece of paper before starting coding or doing Excel. Problem 2 Central Critical Chemical (CCC) manufactures three chemicals: A, B and C. These chemicals are produced via two production processes: 1 and 2. • Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C. • Running process 2 for an hour costs $1 and yields 2 units of A and 1 unit of B. To meet customer demand, at least 6 units of A, 3 units of B, and 1 unit of C must be produced daily. Suppose you are asked to formulate an LP model for CCC to determine an optimal daily production plan (i.e., how many hours should CCC run process 1 and how many hours should CCC run process 2 each day) that minimizes the total cost. (a) Write down LP model and clearly define the decision variables, the objective function, and constraints. (b) Solve the LP model using the graphical method. (c) Provide a justification on why the divisibility assumption holds for the problem.
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