Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
Bartleby Related Questions Icon

Related questions

Question

Read from the image and asnwer the following question:

1- What recipe should the Southfork Feed Company use to minimize cost? 

IMPORTANT: Do not use decimals

Oats : 

Corn :       

Soybean : 

Vitamin  : 

The total cost of this recipe would be : 

2- Which ingredient(s) the company should not use?

Group of answer choices
a-Oats
b-Corn
c-Soybean
d- Vitamin
 
3- Which of the ingredient constraint(s) is(are) binding?
Group of answer choices
a- Oat
b- Corn
c- Soybean
d- Vitamin
 
4-  If they want to invest in procuring extra amounts of one ingredient, which ingredient you recommend they invest in?
Group of answer choices
a- Oat
b- Corn
c- Soybean
d- Vitamin
 
5- If you buy more of this ingredient, what would be the impact on the total cost of the mix?       
a- increase
b- decrease
c- No impact on the spot
 
 
The Southfork Feed Company makes a feed mix from four ingredients: oats, corn, soybeans, and a
vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans,
and 100 pounds of vitamin supplement available for the mix. The company has the following
requirements for the mix:
1] At least 30% of the mix must be soybeans.
2] At least 20% of the mix must be the vitamin supplement.
3] The ratio of corn to oats cannot exceed 2 to 1.
4] The amount of oats cannot exceed the amount of soybeans.
5] The mix must be at least 500 pounds.
A pound of oats costs $0.50; a pound of corn, $1.20; a pound of soybeans, $0.60; and a pound of
vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingre- dient
to put in the mix in order to minimize cost.
Here is the formulation:
x1 is oats, x2 is corn, x3 is soybean and x4 is vitamin supplement
minimize .50x1 +1.20x2 + .60x3 + 2.00x4
subject to
x1 <= 300
x2 <= 400
x3 <= 200
x4
<= 100
-.3x1-.3x2 +.7x3.3x4 >= 0
-.2x1.2x2 .2x3 +.8 x4 >= 0
x22x1 <= 0
x1 x3 <= 0
x1 + x2 + x3 + x4 >= 500
Global optimal solution found.
Objective value:
Infeasibilities:
Total solver iterations:
Elapsed runtime seconds:
Model Class:
Total variables:
Nonlinear variables:
Integer variables:
e
+00
420.0000
0.000000
3
0.12
LP
expand button
Transcribed Image Text:The Southfork Feed Company makes a feed mix from four ingredients: oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: 1] At least 30% of the mix must be soybeans. 2] At least 20% of the mix must be the vitamin supplement. 3] The ratio of corn to oats cannot exceed 2 to 1. 4] The amount of oats cannot exceed the amount of soybeans. 5] The mix must be at least 500 pounds. A pound of oats costs $0.50; a pound of corn, $1.20; a pound of soybeans, $0.60; and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingre- dient to put in the mix in order to minimize cost. Here is the formulation: x1 is oats, x2 is corn, x3 is soybean and x4 is vitamin supplement minimize .50x1 +1.20x2 + .60x3 + 2.00x4 subject to x1 <= 300 x2 <= 400 x3 <= 200 x4 <= 100 -.3x1-.3x2 +.7x3.3x4 >= 0 -.2x1.2x2 .2x3 +.8 x4 >= 0 x22x1 <= 0 x1 x3 <= 0 x1 + x2 + x3 + x4 >= 500 Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: Model Class: Total variables: Nonlinear variables: Integer variables: e +00 420.0000 0.000000 3 0.12 LP
Total constraints:
10
Nonlinear constraints:
Total nonzeros:
Nonlinear nonzeros:
24
е
Variable
x1
Value
200.0000
Reduced Cost
0.000000
x2
0.000000
0.000000
хз
200.0000
0.000000
X4
100.0000
0.000000
Row
slack or Surplus
Dual Price
1
420.0000
2
100.0000
3
400.0000
4
0.000000
5
0.000000
6
50.00000
7
0.000000
8
400.0000
9
10
0.000000
0.000000
-1.000000
e.eeeeee oats constraint
e.eeeeee corn constraint
1.300000 Soybeans constraint
e.eeeeee vitamin constraint
0.000000 At least 30% soybeans
-0.seeeeee At least 20% vitamin
e.eeeeee corn to oats ratio
0.7000000 Oats cannot exceed soybeans
-1.360000 Mix must be at least 500 lbs
Ranges in which the basis is unchanged:
Objective Coefficient Ranges:
Current
Allowable
Allowable
Variable
Coefficient
Increase
Decrease
x1
0.5000000
0.7000000
INFINITY
x2
1.200000
0.8000000
0.6500000
X3
X4
0.6000000
2.eeeeee
1.300000
INFINITY
INFINITY
0.8000000
Righthand side Ranges:
Allowable
Allowable
Current
ROW
RHS
Increase
Decrease
2
300.0000
INFINITY
3
400.0000
INFINITY
100.0000 Oats constraint
400.0000 Corn constraint
4
200.0000
0.000000
5
100.0000
INFINITY
6
0.000000
50.00000
7
0.000000
0.000000
8
0.000000
INFINITY
9
0.000000
0.000000
10
500.0000
0.000000
50.00000 soybeans constraint
0.000000 vitamin constraint
INFINITY At least 30% soybeans
100.0000 At least 20% vitamin
400.0000 Corn to oats ratio
133.3333 Oats cannot exceed soybeans
0.000000 Mix must be at least 500 lbs
expand button
Transcribed Image Text:Total constraints: 10 Nonlinear constraints: Total nonzeros: Nonlinear nonzeros: 24 е Variable x1 Value 200.0000 Reduced Cost 0.000000 x2 0.000000 0.000000 хз 200.0000 0.000000 X4 100.0000 0.000000 Row slack or Surplus Dual Price 1 420.0000 2 100.0000 3 400.0000 4 0.000000 5 0.000000 6 50.00000 7 0.000000 8 400.0000 9 10 0.000000 0.000000 -1.000000 e.eeeeee oats constraint e.eeeeee corn constraint 1.300000 Soybeans constraint e.eeeeee vitamin constraint 0.000000 At least 30% soybeans -0.seeeeee At least 20% vitamin e.eeeeee corn to oats ratio 0.7000000 Oats cannot exceed soybeans -1.360000 Mix must be at least 500 lbs Ranges in which the basis is unchanged: Objective Coefficient Ranges: Current Allowable Allowable Variable Coefficient Increase Decrease x1 0.5000000 0.7000000 INFINITY x2 1.200000 0.8000000 0.6500000 X3 X4 0.6000000 2.eeeeee 1.300000 INFINITY INFINITY 0.8000000 Righthand side Ranges: Allowable Allowable Current ROW RHS Increase Decrease 2 300.0000 INFINITY 3 400.0000 INFINITY 100.0000 Oats constraint 400.0000 Corn constraint 4 200.0000 0.000000 5 100.0000 INFINITY 6 0.000000 50.00000 7 0.000000 0.000000 8 0.000000 INFINITY 9 0.000000 0.000000 10 500.0000 0.000000 50.00000 soybeans constraint 0.000000 vitamin constraint INFINITY At least 30% soybeans 100.0000 At least 20% vitamin 400.0000 Corn to oats ratio 133.3333 Oats cannot exceed soybeans 0.000000 Mix must be at least 500 lbs
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,
Text book image
Operations Management
Operations Management
ISBN:9781259667473
Author:William J Stevenson
Publisher:McGraw-Hill Education
Text book image
Operations and Supply Chain Management (Mcgraw-hi...
Operations Management
ISBN:9781259666100
Author:F. Robert Jacobs, Richard B Chase
Publisher:McGraw-Hill Education
Text book image
Business in Action
Operations Management
ISBN:9780135198100
Author:BOVEE
Publisher:PEARSON CO
Text book image
Purchasing and Supply Chain Management
Operations Management
ISBN:9781285869681
Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:Cengage Learning
Text book image
Production and Operations Analysis, Seventh Editi...
Operations Management
ISBN:9781478623069
Author:Steven Nahmias, Tava Lennon Olsen
Publisher:Waveland Press, Inc.