
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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![A mining company owns two mines, each of which produces three grades (high, medium, and low) of ore.
The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, at least 8
tons of medium-grade ore, and at least 24 tons of low-grade ore. Each hour of operation, mine 1 produces 6
tons of high-grade ore, 2 tons of medium-grade ore, and 4 tons of low-grade ore. Each hour of operation,
mine 2 produces 2 tons of high-grade ore, 2 tons of medium-grade ore, and 12 tons of low-grade ore. It costs
$200 per hour to operate mine 1 and $160 per hour to operate mine 2. How many hours should each mine be
operated so as to meet the contractual obligations at the lowest total operating cost?
U
Microsoft Excel 16.0 Sensitivity Report
2 Worksheet: [2.xlsx]solution
3 Report Created: 10/26/2019 7:20:34 PM
4
5
6 Variable Cells
7
8
9
10
11
12 Constraints
13
Cell
Name
$B$3 X1 Hours to operate Mine 1
$C$3 X2 Hourse to operate Mine 2
Cell
Name
$E$6 High-grade constraint LHS
$E$7 Medium-grade constarint LHS
14
15
16
17 $E$8 Low-grade constarint LHS
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase
Decrease
1
3
12
None of the above
8
0
0
Final Shadow Constraint Allowable
Value Price
R.H. Side Increase
40
10
70
200
160
0
12
8
280
40 93.33333333
24
40
8
4
16
Allowable
Decrease
4
2
1E+30
Use this sensitivity report to answer the questions below.
If the (minimum) requirements increased by 2 tons for each of high-grade, medium-grade, and low-grade
ore: What minimum Cost could be realized? Would the optimal solution change?
The sum of percentages ≥100%, the shadow prices are not operative. Not enough information
provided. Thus, we should create a new model and rerun solver to answer this question.
The sum of percentages ≤ 100%, the shadow prices are operative. The minimum cost would be $840.
The optimal solution will not change.
The sum of percentages ≤ 100%, the shadow prices are operative. The minimum cost would be $840.
The optimal solution would change.](https://content.bartleby.com/qna-images/question/fc1f5cf0-b91a-41d7-a150-55784acf12c2/1414f262-53e7-432a-a67c-41d4d3cc2040/0meh9wk_thumbnail.png)
Transcribed Image Text:A mining company owns two mines, each of which produces three grades (high, medium, and low) of ore.
The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, at least 8
tons of medium-grade ore, and at least 24 tons of low-grade ore. Each hour of operation, mine 1 produces 6
tons of high-grade ore, 2 tons of medium-grade ore, and 4 tons of low-grade ore. Each hour of operation,
mine 2 produces 2 tons of high-grade ore, 2 tons of medium-grade ore, and 12 tons of low-grade ore. It costs
$200 per hour to operate mine 1 and $160 per hour to operate mine 2. How many hours should each mine be
operated so as to meet the contractual obligations at the lowest total operating cost?
U
Microsoft Excel 16.0 Sensitivity Report
2 Worksheet: [2.xlsx]solution
3 Report Created: 10/26/2019 7:20:34 PM
4
5
6 Variable Cells
7
8
9
10
11
12 Constraints
13
Cell
Name
$B$3 X1 Hours to operate Mine 1
$C$3 X2 Hourse to operate Mine 2
Cell
Name
$E$6 High-grade constraint LHS
$E$7 Medium-grade constarint LHS
14
15
16
17 $E$8 Low-grade constarint LHS
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase
Decrease
1
3
12
None of the above
8
0
0
Final Shadow Constraint Allowable
Value Price
R.H. Side Increase
40
10
70
200
160
0
12
8
280
40 93.33333333
24
40
8
4
16
Allowable
Decrease
4
2
1E+30
Use this sensitivity report to answer the questions below.
If the (minimum) requirements increased by 2 tons for each of high-grade, medium-grade, and low-grade
ore: What minimum Cost could be realized? Would the optimal solution change?
The sum of percentages ≥100%, the shadow prices are not operative. Not enough information
provided. Thus, we should create a new model and rerun solver to answer this question.
The sum of percentages ≤ 100%, the shadow prices are operative. The minimum cost would be $840.
The optimal solution will not change.
The sum of percentages ≤ 100%, the shadow prices are operative. The minimum cost would be $840.
The optimal solution would change.
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