A company is manufacturing two products, A and B, at the production facilities in town X and Y. Four customers have ordered the following amounts in the coming period: Product A Produet B 700 Customer I Customer 2 400 550 650 Customer 3 500 800 Customer 4 600 400 The company has currently no products on stock. The products are distributed either directly from the facilities to the customers, or through the intermediate stocks K and L. Both facilities use one unit production time for each of the products and have a total capacity of 2700 time units as shown in the table to the left, while the capacities for the stocks K and L are shown in the table to the right. Time A Time B Capacity 1 Stock K 4000 m Stock L Factory X Factory Y 2700 Сараcity 4500 m Product A Product B 3 m? 2700 Space/unit 2 m² Distribution costs per unit from the production facilities to stocks or customers are: K L 2 3 4 190 160 200 55 65 75 45 150 160 Y 170 210 150 B X 50 70 140 180 150 190 Y 60 40 150 160 200 140 Similarly, the distribution costs from stocks to customers are: 2 130 3 95 K 110 120 85 115 140 75 B K 100 120 90 110 80 110 130 70 Formulate the problem as an LP problem where the main objective is to minimize the costs. Define objective function, constraints, variables and parameters used. i) Find the optimal solution by using Solver in Excel.
A company is manufacturing two products, A and B, at the production facilities in town X and Y. Four customers have ordered the following amounts in the coming period: Product A Produet B 700 Customer I Customer 2 400 550 650 Customer 3 500 800 Customer 4 600 400 The company has currently no products on stock. The products are distributed either directly from the facilities to the customers, or through the intermediate stocks K and L. Both facilities use one unit production time for each of the products and have a total capacity of 2700 time units as shown in the table to the left, while the capacities for the stocks K and L are shown in the table to the right. Time A Time B Capacity 1 Stock K 4000 m Stock L Factory X Factory Y 2700 Сараcity 4500 m Product A Product B 3 m? 2700 Space/unit 2 m² Distribution costs per unit from the production facilities to stocks or customers are: K L 2 3 4 190 160 200 55 65 75 45 150 160 Y 170 210 150 B X 50 70 140 180 150 190 Y 60 40 150 160 200 140 Similarly, the distribution costs from stocks to customers are: 2 130 3 95 K 110 120 85 115 140 75 B K 100 120 90 110 80 110 130 70 Formulate the problem as an LP problem where the main objective is to minimize the costs. Define objective function, constraints, variables and parameters used. i) Find the optimal solution by using Solver in Excel.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:Problem 1
A company is manufacturing two products, A and B, at the production facilities in town X and
Y. Four customers have ordered the following amounts in the coming period:
Product A Product B
Customer 1
Customer 2
700
400
650
550
Customer 3
500
800
Customer 4
600
400
The company has currently no products on stock. The products are distributed either directly
from the facilities to the customers, or through the intermediate stocks K and L.
Both facilities use one unit production time for each of the products and have a total capacity
of 2700 time units as shown in the table to the left, while the capacities for the stocks K and L
are shown in the table to the right.
Time A
Time B Cараcity
Stock K
Stock L
4500 m²
Factory X
Factory Y
2700
Сараeity
4000 m2
2700
Product A
Product B
Space/unit
3 m2
2 m?
Distribution costs per unit from the production facilities to stocks or customers are:
K
L
1
2
3
X
55
75
150
190
160
200
Y
65
45
160
170
210
150
B
50
70
140
180
150
190
60
40
150
160
200
140
Similarly, the distribution costs from stocks
customers are:
A
1
2
3
4
K
110
130
95
120
L
85
115
140
75
В
K
100
120
90
110
80
110
130
70
a)
Formulate the problem as an LP problem where the main objective is to minimize the
costs. Define objective function, constraints, variables and parameters used.
i) Find the optimal solution by using Solver in Excel.
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