Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.
-
Upload
gwendoline-baldwin -
Category
Documents
-
view
213 -
download
1
Transcript of Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.
![Page 1: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/1.jpg)
Holiday Meal Turkey Ranch
Presented by:Olivia OrtegaJen KakacekNikole Ellison
![Page 2: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/2.jpg)
Holiday Meal Turkey Ranch
The Holiday Meal Turkey Ranch is considering buying two different brands of turkey feed and blending them to provide a good, low-cost diet for its turkeys
LetX1 = number of pounds of brand 1 feed purchasedX2 = number of pounds of brand 2 feed purchased Minimize cost (in cents) = 2X1 + 3X2 subject to: 5X1 + 10X2 ≥ 90 ounces (ingredient constraint A) 4X1+ 3X2 ≥ 48 ounces (ingredient constraint B) 0.5X1 ≥ 1.5 ounces (ingredient constraint C) X1≥ 0 (nonnegativity constraint) X2 ≥ 0 (nonnegativity constraint)
![Page 3: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/3.jpg)
Holiday Meal Turkey Ranch
Holiday Meal Turkey Ranch data
INGREDIENT
INGREDIENT
COMPOSITION OF EACH POUND OF FEED (OZ.)
MINIMUM MONTHLY REQUIREMENT PER TURKEY (OZ.)BRAND 1 FEED BRAND 2 FEED
A 5 10 90
B 4 3 48
C 0.5 0 1.5
Cost per pound 2 cents 3 cents
![Page 4: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/4.jpg)
Holiday Meal Turkey Ranch
Using the corner point method
First we construct the feasible solution region
The optimal solution will lie at on of the corners as it would in a maximization problem
–
20 –
15 –
10 –
5 –
0 –
X2
| | | | | |
5 10 15 20 25 X1
Po
un
ds
of
Bra
nd
2
Pounds of Brand 1
Ingredient A Constraint
Ingredient B Constraint
Ingredient C Constraint
Feasible Region
![Page 5: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/5.jpg)
Holiday Meal Turkey Ranch
We solve for the values of the three corner points Point a is the intersection of ingredient constraints C and
B 4X1 + 3X2 = 48 X1 = 3 Substituting 3 in the first equation, we find X2 = 12 Solving for point b with basic algebra we find X1 = 8.4
and X2 = 4.8 Solving for point c we find X1 = 18 and X2 = 0
![Page 6: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/6.jpg)
Holiday Meal Turkey Ranch
Substituting these value back into the objective function we find
Cost = 2X1 + 3X2
Cost at point a = 2(3) + 3(12) = 42Cost at point b = 2(8.4) + 3(4.8) = 31.2Cost at point c = 2(18) + 3(0) = 36
The lowest cost solution is to purchase 8.4 pounds of brand 1 feed and 4.8 pounds of brand 2 feed for a total cost of 31.2 cents per turkey
![Page 7: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/7.jpg)
Holiday Meal Turkey Ranch
Using the isocost approach
Choosing an initial cost of 54 cents, it is clear improvement is possible
–
20 –
15 –
10 –
5 –
0 –
X2
| | | | | |
5 10 15 20 25 X1
Po
un
ds
of
Bra
nd
2
Pounds of Brand 1
(X1 = 8.4, X2 = 4.8)
31.2¢ = 2X1 + 3X
2
Direction of Decreasing Cost
54¢ = 2X1 + 3X
2 Isocost Line
Feasible Region
![Page 8: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/8.jpg)
Holiday Meal Turkey Ranch
Setting up Solver to solve the Holiday Meal Turkey Ranch problem
![Page 9: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/9.jpg)
Holiday Meal Turkey Ranch
Brand 1 Brand 2 Left Handside Right Hand Side Surplus
Objective Function 2 3 0
Ingredient A 5 10 0 >= 90
Ingredient B 4 3 0 >= 48 -48
Ingredient C 0.5 0 0 >= 1.5 -1.5
Solution Values 0 0
![Page 10: Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison.](https://reader036.fdocuments.in/reader036/viewer/2022072005/56649cf05503460f949bf8b1/html5/thumbnails/10.jpg)
Holiday Meal Turkey Ranch
Questions?