Problem 2a
<Back Solver Solution:
Model Formulation: Data:
S T
Z 1.80 2.20
Potassium 5 8 200
Carbohydrate 15 6240
Protein 4 12 180
Decision Variables: S min T 1 10
T
Decision Variables: S T
820
Problem 2b
<Back Solver Solution:
Model Formulation: Data:
x1 x2
Z 2 3
D 4 2 20
E 2 6 18
Decision Variables: x1 F 1 2 12
x2
Decision Variables: x1 x2
4.2 1.6
Objective Function: Minimize 2 x1 + 3 x2 Objective Function: Minimize 13.2
Problem 3
<Back Solver Solution:
Model Formulation: Data:
H W
Profit per Unit 40 30 Available
Fabrication 4 2 600
Assembly 2 6 480
Decision Variables: H = number of model W
W = number of model H Decision Variables: H W
132 36
Problem 4
<Back Solver Solution:
Model Formulation: Data:
x1 x2
Revenuet per Unit 2.90 2.55
Profit per Unit 1.70 1.50 Available Cost
raisins 0.67 0.50 90 1.50
peanuts 0.33 0.50 60 0.60
max x1 1 0 110
max x2 0 1 110
Decision Variables: x1 = bags of deluxe mix
x2 = bags of standard mix Decision Variables: x1 x2
90 60
Problem 5
<Back Solver Solution:
Model Formulation: Data:
x1 x2
Revenue per Unit 1.50 1.20 Available
Sugar 1.5 2.0 1,200
Flour 3.0 3.0 2,100
Time 6 3 3,600
Decision Variables: x1 = number of apple pies
x2 = number of grape pies Decision Variables: x1 x2
500 200
Problems 6a, 7a, 8a
<Back Solver Solution:
Model Formulation: Data:
x1 x2 x3
Z 4 2 5
1 2 1 25
1 4 2 40
Decision Variables: x1 3 3 1 30
x2
x3 Decision Variables: x1 x2 x3
4 0 18
Microsoft Excel 14.0 Sensitivity Report
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost
Coefficient
Increase Decrease
$I$11 x1 4 0 4 11 1.5
$J$11 x2 0 -8.6 2 8.6 1E+30
$K$11 x3 18 0 5 3 3.666666667
Problems 6b, 7b, 8b
<Back Solver Solution:
Model Formulation: Data:
x1 x2 x3
Z 10 6 3
11225
21440
Decision Variables: x1 12340
x2
x3 Decision Variables: x1 x2 x3
15 10 0
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost
Coefficient
Increase Decrease
$I$11 x1 15 010 2 4
$J$11 x2 10 0 6 4 1
$K$11 x3 0 -17 3 17 1E+30
Coefficient
Problem 10
<Back Solver Solution:
Model Formulation: Data:
Price per Unit
Profit per Unit
Orange Juice
Grapefruit Juice
Pineapple Juice
Max orange juice
Objective Function: Maximize .50 x1 + .50 x2 + .45 x3 + Objective Function:
.6833 x4
Constraints:
Constraints: Subject To:
x1 x2 x3 x4
1.00 0.90 0.80 1.10
0.250 0.000 0.000 0.083 400 2.00
0.000 0.250 0.000 0.083 300 1.60
0.000 0.000 0.250 0.083 200 1.40
5-7 0
x1 x2 x3 x4
800.00 400.00 0.00 2400.00
Maximize 2240.00
Subject To: Slack/
Surplus
ange Juice 400
≤400 -5.7E-14
≤300 0
≤200 -5.7E-14
Problem 11
<Back Solver Solution:
Model Formulation: Data:
x1
Profit per Unit 2
Machine 1.4
Labor 5
Product 2 12
Decision Variables: x1 = quantity of chopping blocks
x2 = quantity of knife holders Decision Variables: x1
0
x2
6 Available
0.8 56
13 650
3360
x2
50
Problem 12
<Back a. Solver Solution:
a. Model Formulation: Data:
x1 x2
Cost per Unit 3 3 Available
Mayonaise 1.4 1.0 70
Decision Variables: x1 x2
37.14 18.00
Objective Function: Minimize 3 x1 + 3 x2 Objective Function: Minimize 165.4286
Constraints: Subject To: Constraints: Subject To: Slack/
Surplus
Mayonaise 1.4 x1 + 1 x2 >= 70 Mayonaise 70
≥70 0
≥20 17.14286
b. Solver Solution:
b. Model Formulation: Data:
x1 x2
Profit per Unit 2 4 Available
Mayonaise 1.4 1.0 112
Decision Variables: x1 x2
20 84
Objective Function: Maximize 2 x1 + 4 x2 Objective Function: Maximize 376
Problem 13
<Back Solver Solution:
Model Formulation: Data:
A B C
Revenue 80 90 70
Profit per Unit 26 50 20 Available Cost
Material 1 2 1 6 200 5
B = units of product B
C = units of product C Decision Variables: A B C
18.75 12.50 25.00
Objective Function: Maximize 26 A + 50 B + 20 C Objective Function: Maximize 1612.50
Constraints: Subject To: Constraints: Subject To: Slack/
Surplus
Material 1 2 A + B + 6 C ≤ 200 Material 1 200
≤200 0
≤300 181.25
≤150 21.25
Material 2 3 5 0 300 4
Problem 14
<Back Solver Solution:
Model Formulation: Data:
x1 x2 x3 x4 x5 x6 Available
Profit per box 0.80 0.90 0.70 0.60 0.50 0.75
Cashews 0.25 0.50 1.00 120
Raisins 0.25 1.00 200
Decision Variables: x1 = boxes of regular mix Carmels 0.25 1.00 100
x2 = boxes of deluxe mix Chocolates 0.25 0.50 1.00 160
Objective Function:
aximize
.80 x1 + .90 x2 + .70 x3 +
.60 x4 + .50 x5 + .75 x6 Objective Function: Maximize 433
Constraints: Subject To: Constraints: Subject To: Slack/
Surplus
Cashews .25 x1 + .50 x2 + x3 ≤ 120 Cashews 120
≤120 0
Raisins .25 x1 + x4 ≤ 200 Raisins 200
≤200 0
≤100 0
≤160 0
x3 = boxes of cashews Min Boxes 20
x5 = boxes of carmels Decision Variables: x1 x2 x3 x4 x5 x6
x6 = boxes of chocolates 320 40 20 120 20 60
Problem 15
<Back Solver Solution:
Model Formulation: Data:
x1 x2 x3
Profit per Unit 12 18 15 Available
Machine 5 4 3 160
Labor 4 10 4288
Objective Function: Maximize 12 x1 +18 x2 + 15 x3 Objective Function: Maximize 792
Constraints: Subject To: Constraints: Subject To: Slack/
Surplus
Machine 5 x1 + 4 x2 + 3 x3 ≤ 160 Machine 160
≤160 0
≤288 56
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost
Coefficient
Increase Decrease
$I$12 x1 0 -10.2 12 10.2 1E+30
$J$12 x2 4 0 18 2 7.285714
$K$12 x3 48 015 21 1.5
Problem 16
<Back Solver Solution:
Model Formulation: Data:
x1 x2 x3
Profit per Unit 9 9 6 Available
Bark 5 6 3 600
Objective Function: Maximize 9 x1 + 9 x2 + 6 x3 Objective Function: Maximize 1125
Constraints: Subject To: Constraints: Subject To: Slack/
Surplus
Bark 5 x1 + 6 x2 + 3 x3 ≤ 600 Bark 600
≤600 0
Machine 2 x1 + 4 x2 + 5 x3 ≤ 600 Machine 525
≤600 75
Labor 2 x1 + 4 x2 + 3 x3 ≤ 480 Labor 375
≤480 105
Storage 1 x1 + 1 x2 + 1 x3 ≤ 150 Storage 150 ≤150 0
non-negativity x1, x2, x3 ≥ 0
Microsoft Excel 14.0 Sensitivity Report
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost
Coefficient
Increase Decrease
$I$12 x1 75 0911
$J$12 x2 0 -1.5 9 1.5 1E+30
$K$12 x3 75 0 6 3 0.6