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 8 10 100 VitC 6 10 15 15 4 120 100 Calc 30 20 25 15 15 20 30 100 Iron 20 20 20 10 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.

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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Question

Must be done win excell

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
8
4
10
100
VitC
10
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.
2.
2.

Expert Solution

Objective Functions and Constraints:

Objective Functions and Constraints:

Based on the given details, the objective functions and constraints are

Objective Function:

$M i n c = 3.79 x_{1} + 4.49 x_{2} + 3.99 x_{3} + 3.79 x_{4} + 1.29 x_{5} + 1.79 x_{6} + 1.19 x_{7} + 1.00 x_{8} + 1.89 x_{9} x_{1} - Q P x_{2} - A D x_{3} - B M x_{4} - F F x_{5} - M C x_{6} - F R x_{7} - S M x_{8} - 1 M x_{9} - O J$

Constraints:

Subject to

$P r o t : 28 x_{1} + 24 x_{2} + 25 x_{3} + 14 x_{4} + 31 x_{5} + 3 x_{6} + 15 x_{7} + 9 x_{8} + 1 x_{9} \geq 55 V i t A : 15 x_{1} + 15 x_{2} + 6 x_{3} + 2 x_{4} + 8 x_{5} + 0 x_{6} + 4 x_{7} + 10 x_{8} + 2 x_{9} \geq 100 V i t C : 6 x_{1} + 10 x_{2} + 2 x_{3} + 0 x_{4} + 15 x_{5} + 15 x_{6} + 0 x_{7} + 4 x_{8} + 120 x_{9} \geq 100 C a l c : 30 x_{1} + 20 x_{2} + 25 x_{3} + 15 x_{4} + 15 x_{5} + 0 x_{6} + 20 x_{7} + 30 x_{8} + 2 x_{9} \geq 100 I r o n : 20 x_{1} + 20 x_{2} + 20 x_{3} + 10 x_{4} + 8 x_{5} + 2 x_{6} + 15 x_{7} + 0 x_{8} + 2 x_{9} \geq 100 C a l s : 510 x_{1} + 370 x_{2} + 500 x_{3} + 370 x_{4} + 400 x_{5} + 220 x_{6} + 345 x_{7} + 110 x_{8} + 80 x_{9} \geq 2000 C a r b : 34 x_{1} + 33 x_{2} + 42 x_{3} + 38 x_{4} + 42 x_{5} + 26 x_{6} + 27 x_{7} + 12 x_{8} + 20 x_{9} \geq 350 x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, x_{9} \geq 0$