Question: Problem 10-11 The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit
Problem 10-11
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows:
Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows:
Formulate a linear programming model of the problem. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Let Xij represents relation between plants to warehouses or relation between warehouses to customers.
| MIN | __________X14+_________X15+________X24+__________X25+_________X34+_____________X35+___________X46+_______X47+_________X48+________X49+________X56+_________X57+_________X58+_________X59 |
| S.T. | |||||||||||||||
| 1) | fill in the blank 16X14 | + | fill in the blank 17X15 | < | fill in the blank 18 | ||||||||||
| 2) | fill in the blank 19X24 | + | fill in the blank 20X25 | < | fill in the blank 21 | ||||||||||
| 3) | fill in the blank 22X34 | + | fill in the blank 23X35 | < | fill in the blank 24 | ||||||||||
| 4) | fill in the blank 25X46 | + | fill in the blank 26X47 | + | fill in the blank 27X48 | + | fill in the blank 28X49 | + | fill in the blank 29X14 | + | fill in the blank 30X24 | + | fill in the blank 31X34 | = | fill in the blank 32 |
| 5) | fill in the blank 33X56 | + | fill in the blank 34X57 | + | fill in the blank 35X58 | + | fill in the blank 36X59 | + | fill in the blank 37X15 | + | fill in the blank 38X25 | + | fill in the blank 39X35 | = | fill in the blank 40 |
| 6) | fill in the blank 41X46 | + | fill in the blank 42X56 | = | fill in the blank 43 | ||||||||||
| 7) | fill in the blank 44X47 | + | fill in the blank 45X57 | = | fill in the blank 46 | ||||||||||
| 8) | fill in the blank 47X48 | + | fill in the blank 48X58 | = | fill in the blank 49 | ||||||||||
| 9) | fill in the blank 50X49 | + | fill in the blank 51X59 | = | fill in the blank 52 |
- Solve the linear program to determine the optimal shipping plan. Objective Function Value = fill in the blank 53
There is an excess capacity of ___________units at plant 1plant, 2plant, 3plant .Variable Value Reduced Costs X14 X15 X24 X25 X34 X35 X46 X47 X48 X49 X56 X57 X58 X59
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