Theatre Design & Technology - Spring 1975 - 24

20

K

-1000+200 (f/p,10%, 20) (p/f ,15% ,20) -

L20

(1.1) n (p/f ,15% ,n)

1

-1000+200(i: i~r20 [:

[1. lOr
1.15

1J

[1.10]
1.15

-1177 .

The present worth of the Frek investment is
3

F

-250- L22S(f/P,10%,Sn) (p/f,lS%,Sn) + 2S(f/p,10%,20) (p/f,lS%,20)
I

20

- L 30 (1.1)n(p/f,lS%,n)
I

-250-225

[6.

(1.10'~_30

10':.5+ (1.10':
\1.15) \1.15) \1.15)J

=--------=<-~:
~~21 _
10]
b··1.15]

[_1
1 _

J

+25 (_1.10)20
1.15

F = -1068.
Since the present cost of the Kerf investment ($1177) is
more than the present cost of the alternative sequence of Frek
investments ($1068), the purchase and operation of one Kerf
saw over the next 20 years will be more expensive than the
purchase and operation of four consecutive Frek saws over the
same period. In the absence of additional information, the Frek
saw must therefore be considered the better buy.
We have assumed that the operating costs for saw blades,
labor, and electric power will be the same for both machines.
Many other reasonable assumptions are implicit by convention
in simple engineering economy studies, such as the presumption that maintenance expenditure occurs at the end of each
year. Such implicit assumptions can be removed in the unusual
event that they are inappropriate, of course, but at the expense
of complicating the analysis. Expectations about the rate of
inflation and statistical variability in periodic costs are among
the uncertainties which can also be explicitly accounted for in
such an analysis if there is reason to expect that they wou Id
affect the conclusion. Some doubt must, of course, accompany
any decision which rests upon predictions of the economic
future, but business experience in many industries has shown
that even simple analyses usually save money.

Technical Production. Quantitative methods can
often assist common sense in the planning and
direction of performance processes such as the
transmission and execution of lighting and sound
cues, the operation of set machinery, and the
movement and storage of scenery, props, and
costumes.

24

~

Illustrative Example. The four acts of a production require
settings, a, b, and c to be used in the order abcb. In
preparation for the first act of the next performance, of course,
setting b must be struck and replaced by setting a. The two
sets which are not in use during an act are stored in a wing of
the stage house. Because of the sizes and shapes of the set
pieces and the wing space, set b cannot be 3tored with set a or
set c except in such a way that only it or the other set is directly
accessible, but not both. Whenever set b is stored with another
set, the accessible set must be moved out of storage before the
other set can be shifted. There is room on the stage for the
pieces of all three sets to be temporarily stored during scene
changes between the acts, but the three sets will not fit into the
wing space together. Find a shift sequence which minimizes
the number of sets which must be moved in the course of a
long run of the production.
Solution. Designate an arrangement of setting in place and
in storage by the ordered triple (set in place, set in storage 1,
set in storage 2). If set b is in storage, the accesible set is in
storage 1. There are 3! 6 possible arrangements of sets
during the performance of an act, and each can be reached
from any of the others by moving a certain number of sets.
For example, to change from (a,b,c) to (b,a,c), three sets must
be moved, while four sets must be moved to change from
(a,b,c,) to (b,c,a). The first act requires either arrangement
(a,b,c) or arrangement (a,c,b), so that set a will be in place on
stage. A suitable arrangement for each of the other acts must
similarly be one or the other of the two possible arrangements
which locate the appropriate set on stage. We can summarize
the situation with the diagram shown below.

=

THEATRE DESIGN AND TECHNOLOGY

SPRING. 1975
Table of Contents for the Digital Edition of Theatre Design & Technology - Spring 1975
