Exercises

2 exercises

Exercise 2: Use the shortest path algorithm and the minimum spanning tree algorithm for each
of these networks:
a.
Distance Between Pairs of Locations
O
A
B
C
D
E
F
T
O
–
3
5
4
–
–
–
–
A
3
–
4
–
7
–
–
–
B
5
4
–
1
3
–
–
–
C
4
–
1
–
5
4
6
–
D
–
7
3
5
–
2
3
–
E
–
–
–
4
2
–
1
6
F
–
–
–
6
3
1
–
4
T
–
–
–
–
–
6
4
–
b.
Distance Between Pairs of Locations
O
A
B
C
D
E
F
G
H
I
T
O
–
2
3
2
–
–
–
–
–
–
–
A
2
–
–
1
4
–
–
–
–
–
–
B
3
–
–
2
–
3
–
–
–
–
–
C
2
1
2
–
3
4
2
–
–
–
–
D
–
4
–
3
–
–
3
4
–
–
–
E
–
–
3
4
–
–
3
–
5
4
–
F
–
–
–
2
3
3
–
5
6
–
–
G
–
–
–
–
4
–
5
–
3
–
6
H
–
–
–
–
–
5
6
3
–
3
5
I
–
–
–
–
–
4
–
–
3
–
8
T
–
–
–
–
–
–
–
6
5
8
–
The Fly-Right Airplane Company builds small jet airplanes to sell to corporations for the use of
their executives. To meet the needs of these executives, the company’s customers sometimes order
a custom design of the airplanes being purchased. When this occurs, a substantial start-up cost is
incurred to initiate the production of these airplanes. Fly-Right has recently received purchase
requests from three customers with short deadlines. However, because the company’s production
facilities already are almost completely tied up filling previous orders, it will not be able to accept
all three orders. Therefore, a decision now needs to be made on the number of airplanes the
company will agree to produce (if any) for each of the three customers. The relevant data are given
in the next table. The first row gives the start-up cost required to initiate the production of the
airplanes for each customer. Once production is under way, the marginal net revenue (which is the
purchase price minus the marginal production cost) from each airplane produced is shown in the
second row. The third row gives the percentage of the available production capacity that would be
used for each airplane produced. The last row indicates the maximum number of airplanes
requested by each customer (but less will be accepted).
Customer
1
2
3
Start-up cost
$3 million
$2 million
0
Marginal net revenue
$2 million
$3 million
$0.8 million
Capacity used per plane
20%
40%
20%
Maximum order
3 planes
2 planes
5 planes
Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to
maximize the company’s total profit (total net revenue minus start-up costs).
a. Formulate a model with both integer variables and binary variables for this problem.
Use the computer to solve this model