A florist provides fresh flowers to shops in Wollongong. At present she has one nursery in Goulburn with capacity 9000 units a year. The florist is considering opening shops in Canberra and Sydney, and has found three potential nursery sites at Wagga, Orange and Bathurst. The transportation tableau below summarises the projected nursery capacities (units), the cost per unit of shipping from each nursery to each destination (dollars), and the demand (units) for the coming year. j1 j-2 Wollongong Canberra 5 i-1 Goulburn 1-2 Wagga 1-3 Orange 1-4 Bathurst 11000 7 $180,000 $160,000 $270,000 13 16 8 5 6 12 j-3 Sydney 12 8000 10 4 2 Capacities 9000 4000 Demand 5000 There are further constraints on how the nurseries can be located: • If a nursery is located in Wagga, another must be located in Bathurst and vice- versa. • One nursery can be located in Orange or Bathurst, but not both Suppose that the costs of establishing new nurseries are Wagga Orange Bathurst 7000 11000 The goal is to develop a 0-1 mixed-integer linear programming model to minimise the total cost of establishing new nurseries and distributing units to shops. You are not required to solve the problem. a. Introduce symbols for each variable needed in the problem and briefly state what they correspond to. b. Define the objective function in terms of your variables, and the goal for the objective function. c. Write down all constraints for the problem in terms of your variables. Beside each constraint, briefly describe what it represents in terms of the original problem.
A florist provides fresh flowers to shops in Wollongong. At present she has one nursery in Goulburn with capacity 9000 units a year. The florist is considering opening shops in Canberra and Sydney, and has found three potential nursery sites at Wagga, Orange and Bathurst. The transportation tableau below summarises the projected nursery capacities (units), the cost per unit of shipping from each nursery to each destination (dollars), and the demand (units) for the coming year. j1 j-2 Wollongong Canberra 5 i-1 Goulburn 1-2 Wagga 1-3 Orange 1-4 Bathurst 11000 7 $180,000 $160,000 $270,000 13 16 8 5 6 12 j-3 Sydney 12 8000 10 4 2 Capacities 9000 4000 Demand 5000 There are further constraints on how the nurseries can be located: • If a nursery is located in Wagga, another must be located in Bathurst and vice- versa. • One nursery can be located in Orange or Bathurst, but not both Suppose that the costs of establishing new nurseries are Wagga Orange Bathurst 7000 11000 The goal is to develop a 0-1 mixed-integer linear programming model to minimise the total cost of establishing new nurseries and distributing units to shops. You are not required to solve the problem. a. Introduce symbols for each variable needed in the problem and briefly state what they correspond to. b. Define the objective function in terms of your variables, and the goal for the objective function. c. Write down all constraints for the problem in terms of your variables. Beside each constraint, briefly describe what it represents in terms of the original problem.
Chapter6: Systems Of Equations And Inequalities
Section6.5: Systems Of Inequalities
Problem 9ECP
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Transcribed Image Text:A florist provides fresh flowers to shops in Wollongong. At present she has one nursery
in Goulburn with capacity 9000 units a year. The florist is considering opening shops in
Canberra and Sydney, and has found three potential nursery sites at Wagga, Orange and
Bathurst. The transportation tableau below summarises the projected nursery capacities
(units), the cost per unit of shipping from each nursery to each destination (dollars), and
the demand (units) for the coming year.
j=1
j=2
j=3
Sydney
Capacities
Wollongong Canberral
5
i=1 Goulburn
12
9000
i=2 Wagga
7
10
4000
i=3 Orange
4
7000
i=4 Bathurst
11000
Demand
11000
5000
8000
There are further constraints on how the nurseries can be located:
• If a nursery is located in Wagga, another must be located in Bathurst and vice-
versa.
•
One nursery can be located in Orange or Bathurst, but not both.
Suppose that the costs of establishing new nurseries are
Wagga
$180,000
Orange
$160,000
Bathurst
$270,000
The goal is to develop a 0-1 mixed-integer linear programming model to minimise the
total cost of establishing new nurseries and distributing units to shops. You are not
required to solve the problem
a. Introduce symbols for each variable needed in the problem and briefly state what
they correspond to.
b. Define the objective function in terms of your variables, and the goal for the
objective function.
c. Write down all constraints for the problem in terms of your variables. Beside each
constraint, briefly describe what it represents in terms of the original problem.
13
16
8
5
6
12
2
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