The Move-It Company has two plants producing forklift trucks that then are shipped to three distribution
centers. The production costs are the same at the two plants, and the cost of shipping for each truck is
shown for each combination of plant and distribution center:

A total of 60 forklift trucks are produced and shipped per week. Each plant can produce and ship any
amount up to a maximum of 50 trucks per week, so there is considerable flexibility on how to divide the
total production between the two plants so as to reduce shipping costs. However, each distribution center
must receive exactly 20 trucks per week.
Managements objective is to determine how many forklift trucks should be produced at each plant, and
then what the overall shipping pattern should be to minimize total shipping cost

a) The mathematical formulation:
Please show all work. All the constrains, objective equation, labelsetc more info the better.

?
b) The optimal solution using Excel.
BELOW IS THE ANSWER. BUT ITS NOT SOLVED BY USING SOLVER IN
EXCEL. IF YOU CAN SOLVE IT IN EXCEL USING SOLVER THAT WOULD BE
GREAT, Shouldnt take long since everything is already setup. If not, Mathematical
formulations work is what I am mainly looking for.
Distri
bution
Center
s (cost
x 100)

1
Plant

2

3

8

7

4

Dumm
Supply
y
0
50

Ui
0

A
Plant
B
Deman
d
Vj

6

8

4

0

20

20

20

40

6

8

5

50

0

0

Distri
bution
Center
s
1
Plant
A
Plant
B
Deman
d
Vj

2

3
20

Dumm
Supply
y

Ui

30

50

0

10

50

1

20

20

20

20

20

40

5

7

4

0

Distri
bution
Center
s
1
Plant
A
Plant
B
Deman
d
Vj

2

3

20

20

Dumm
Supply
y

Ui

50

0

30

20

10

50

0

20

20

20

40

6

8

4

0

Total Cost (x100)

$340

C= 600(20) +700(20) +400(20) +0(10) +0(30) = $ 34,000

_______________________________ Multiple Choice _______________________________

1.

Consider a minimal spanning tree problem in which pipe must be laid to connect sprinklers on a
golf course. When represented with a network,
a.
the pipes are the arcs and the sprinklers are the nodes.
b.
the pipes are the nodes and the sprinklers are the arcs.
c.
the pipes and the sprinklers are the tree.
d.
each sprinkler must be connected to every other sprinkler.

2.

Which would be the correct transformation for the constraints defined as:
ax1+bx2 c; x1-d; x20.
a.
b.
c.
d.

3.

a(x1+d)+bx2x3+ x4=c; xj0 (j=1,..,4)
ax1+bx2x3+x4=c; x1+x5 =d; xj0 (j=1,..,5)
ax1+bx2x3+x4=c; x1x5+x6=-d; xj0 (j=1,..,6)
ax1+bx2+x3x4=c; x1+x5=-d; xj0 (j=1,..,5)

The shortest-route algorithm has assigned the following permanent labels to six nodes, where the
label [a, b] indicates the minimum distance a up to the node k from node b.
Node
Label
1
[0,S]
2
[15,1]
3
[12,1]
4
[20,3]
5
[8,1]
6
[32,4]
What is the shortest path from the source to node 6?
a.
1, 3, 4, 6
b.
1, 6
c.
1, 2, 5, 6
d.
1, 5, 6

4.

The basic solution to a problem with four equations and five variables would assign a value of 0
to
a.
b.
c.
d.

4 variables.
0 variables.
1 variable.
7 variables.

5.

Given a maximization problem with the following intermediate simplex tableau:
Basic
Variab
le
z
x1
x5
x2

Eq.
0
1
2
3

Coeffi
cient
of
z
1
0
0
0

RHS
x1
0
1
0
0

x2
0
0
0
1

x3
-4
-1
-5
0

x4
-3
3
1
7

x5
0
0
1
0

Which statement is true?
a.
b.
c.
d.

The problem may have an unbounded feasible region.
x3 enters to the basis and x5 leaves the basis.
x4 enters to the basis and x2 leaves the basis.
It cannot be determined since there is missed information.

20
4
14
2