Matrix Accounting Illustrated: Contribution Margin

 Published date 01 July 2016 Date 01 July 2016 DOI http://doi.org/10.1002/jcaf.22180
59
© 2016 Wiley Periodicals, Inc.
Published online in Wiley Online Library (wileyonlinelibrary.com).
DOI 10.1002/jcaf.22180
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Matrix Accounting Illustrated:
Contribution Margin
Melvin Hughes
INTRODUCTION
useful to put it side-
by-side with the pre-
ceding article (“The
Simple Analytics of
Matrix Account-
ing, Activity-Based
Costing and Linear
Programming”).
the whole article, it may be use-
ful to look over the summary in
the appendix.
Here, I intend to make
good on my promise that the
analytics are simple. I said
that a typical executive chef
could use this model, so we
will go over the steps on the
computer in detail. This paper
stops before the discussion of
activity-based costing (ABC)
and linear programming (LP).
The second section reviews
some notation of matrix alge-
bra and reviews the matrices we
will be using. The third section
builds a case study of Coase
Vineyards, a small winery in
Napa Valley, California. This
is a good example, in that for
wineries, prices and quality
of grapes varies year by year.
The product mix can change
very often, and small winer-
ies don’t have the resources to
build specialized but inefficient
computer models of costs.
Even large wineries with cost
accounting software in place
may find this material
beneficial.
The fourth section builds
an example of a hotel banquet
kitchen, which again has vary-
ing costs of inputs. For brev-
ity, I do not include a separate
numerical example, but just
provide a verbal discussion of
how the hotel industry could
use the Activity-Based Linear
Economic Model (ABLEM)
for real-time price negotiations
in a fast-paced setting.
The final section
suggests further uses
of ABLEM by man-
agerial accountant.
The third article is
introduced, describ-
ing how manage-
rial accounting and
operations research
can be integrated
with the present
mathematical model
of the firm.
REVIEW OF MATRIX NOTATION
AND MODEL VARIABLES
Before reviewing matrix
notation, I have duplicated the
parts of the appendix from
the first article that we will be
using in the current article.
Recall that the indexing num-
bers are M = the number of
products used, and N = the
number of variable inputs.
Recall that matrices are
boxes of numbers. Let us look
at the matrix S, the standard
usages of variable inputs.
When we say that it is a N ×
M matrix, we are saying that
it has N rows and M columns.
The “element” of the matrix
s23 would be the number in the