Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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- A manufacturer produces bicycles and motorcycles, each of which must be processed through two machine centers. Machine center 1 has a maximum of 120 hours available and machine center 2 has a maximum of 180 hours available. A bicycle requires 6 hours in mc1 and 3 hours in mc2. Manufacturing a motorcycle requires 4 hours in mc1 and 10 hours in mc2. If the profit is $45 for each bicycle and $250 for a motorcycle, determine the number of bicycles and number of motorcycles to produce to maximize profit considering that the number of motorcycles must not exceed 12 units and bicycle must be at least 10 units. Formulate as Linear Program and solve using the graphical Method.
-
Solve using LP-Simplex Solution
Maximize Z = 10X1 + 14X2
Subject to:
4x1 + 6x2 <= 24
2x1 + 6x2 <= 20
x1, x2 >= 0
- Consider the transportation problem given below.
Destinations
Source
1
2
3
Supplies
1
9
6
4
5
2
4
10
2
6
3
15
7
10
5
Demands
9
3
4
16
- Construct the NW corner solution
- Compute the total cost of the NW corner solution
- Using the stepping stone method, find the min-cost solution.
4. Assignment Problem. Maximize Profit
|
|
Machines |
|||
|
Worker |
1 |
2 |
3 |
4 |
|
A |
12 |
15 |
11 |
14 |
|
B |
10 |
12 |
11 |
10 |
|
C |
13 |
12 |
15 |
15 |
|
D |
13 |
13 |
14 |
14 |
Transcribed Image Text:1. A manufacturer produces bicycles and motorcycles, each of which must be
processed through two machine centers. Machine center 1 has a maximum of 120
hours available and machine center 2 has a maximum of 180 hours available. A bicycle
requires 6 hours in mc1 and 3 hours in mc2. Manufacturing a motorcycle requires 4
hours in mc1 and 10 hours in mc2. If the profit is $45 for each bicycle and $250 for a
motorcycle, determine the number of bicycles and number of motorcycles to produce to
maximize profit considering that the number of motorcycles must not exceed 12 units
and bicycle must be at least 10 units. Formulate as Linear Program and solve using the
graphical Method.
2. Solve using LP-Simplex Solution
Maximize Z = 10X1 + 14X2
Subject to:
4x1 + 6x2 <= 24
2x1 + 6x2 <= 20
х1, х2 >3 0
3. Consider the transportation problem given below.
Destinations
Source
1
3
Supplies
1
9
6
4
4
10
3
15
7
10
Demands
3
4
16
a. Construct the NW corner solution
b. Compute the total cost of the NW corner solution
c. Using the stepping stone method, find the min-cost solution.
4. Assignment Problem. Maximize Profit
Machines
Worker
1
3
4
A
12
15
11
14
В
10
12
11
10
C
13
12
15
15
13
13
14
14
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