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1. ANALYSIS ON A’S LAUNDRY SHOP: A PROFIT MAXIMIZATION APPROACH
Laureta, Rutchiel D.
Morales, Dianne D.
Ricalde, Ruby Grace J.
Bachelor of Science in Agribusiness Economics
University of the Philippines
Mindanao
December 2014
1
A research paper submitted in partial fulfillment of the requirements in Economics 130 –
Elements of Mathematical Economics, under the advisory of Mr. Jon Marx Sarmiento, First
Semester, A.Y. 2014-2015.

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TABLE OF CONTENTS
I. TITLE PAGE
II. ABSTRACT
III. TABLE OF CONTENTS
IV. INTRODUCTION
i. Background of the Study
ii. Significance of the Study
iii. Objectives
iv. Scopes and Limitation
V. METHODOLOGY
i. Data Source
ii. Data Analysis
VI. RESULTS AND DISCUSSION
i. Data Modeling
ii. Profit Maximization
iii. Hessian Matrix
VII. SUMMARY AND CONCLUSION
VIII. RECOMMENDATION
IX. APPENDIX
X. REFERENCE

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ABSTRACT
Laundry is one of the biggest contributors of service in the Philippines, comprising 6%
of the sector. This type of business has been sprouting out in Davao City, even in the far flung
area of Mintal. A quantitative and qualitative analysis was done on one of the laundry shops
located in the heart of Mintal, which is A’s Laundry Shop. This study aims to find out the
maximum profit, to identify the best combination of the amount of labor and capital to produce
maximum profit, to determine the maximum number of kilograms to be washed per month that
would maximize the profit and to provide recommendation to the owners. Data was gathered
through an interview and were organized through Microsoft Excel and were run through Gretl
and Lingo. Results showed that A’s Laundry Shop can attain their maximum profit of Php38,
694.31 in present time by inputting Php13,978.71 of capital and Php5,626.773 of labor per
month. This combination of inputs can generate an output of 2914.989454 kilos of laundry.
A’s Laundry Shop should also hire an average of 1.35 or 1 to 2 laborers per day in order to
attain the maximum profit. These number of laborers were already being practiced by the firm.
Thus, there’s no need to hire additional workers. Moreover, A’s Laundry Shop must reach
and/or limit their amount of input in Php13, 978.71 every month to attain the maximum profit.
The researchers conducted SWOT analysis to recommend the best strategies. A’s Laundry
Shop should expand the business, invest in technological resources, conduct advertisements
and be open and ready to entertain vast external orders from households.

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I. INTRODUCTION
i. Background of the Study
The Philippines is a country known to provide services rather than manufactured
goods. In fact, services sector is the one that drives our economy. The share of the service
sector in GDP has exceeded that of the industry sector since the mid-1980s growing from
36% to 55% in 2010, and the sector’s share in total employment increased from 40% in
1990 to 52% in 2010. The service sector share of GDP has continued to increase in recent
years. It rose from 54.1% in 2006 to 57.1% in 2012 as shown in Table 1 (Asian
Development Bank, 2013).

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One of the most common providers of services in the country is the laundry services.
In fact, it provides 6.0% of the total employment in the sector, which is a significant
percentage. The data is shown in Figure 1.
Fig.1. Percent Distribution of Employment by Industry Group by year 2010.
Source: Annual Survey Philippine Business and Industry (ASBPI) and Other Service Activities NSO, 2012
Seeing that the laundry service is significant in the Philippine setting, this type of
businesses has been sprouting out in Davao City. Even in the far flung area of Mintal, a number
of laundry shops can be seen. Mintal is also seen as a strategic place for this business since it
houses many schools, including the University of the Philippines Mindanao. Since most of the
students cannot go home nor have the time to wash their own clothes, this proves to be a
profitable business. The profitability of this business is dependent on the cost of inputs used,
which include detergent powder, detergent bar, fabric conditioner, energy and water bills. A’s
Laundry Shop is one of the places that students go to have their clothes washed. As requested
by the owners, the researchers kept the name of the shop confidential. Located at a strategic
place in Mintal, it is accessible to people, may it be students, homeowners, workers, etc.

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ii. Objectives
A. To model the Cobb-Douglas Production Function of A’s Laundry Shop;
B. To identify the best combination of amount of labor and capital to produce
maximum profit;
C. To determine the maximum number of kilograms washed per month that
would maximize the profit; and
D. To provide recommendations to the owner.
iii. Significance of the Study
This study wants to assess the performance of A’s Laundry Shop by using profit
maximization approach and to provide the optimal utilization of the factors that affect
their production to somehow maximize their profit. Results of this study would help the
owner to implement actions and decisions to utilize their capital and to know the
number of laborers that they should hire.
iv. Scope and Limitations
The study is focused only on the operation, specifically the cost and production
of A’s Laundry Shop. The researchers only considered capital and labor as the factors
for quantity produced. Moreover, this study assumes that all the laundry washed were
colored type cloths that amounts Php20 per kilo, not accounting the white type ones
that costs higher.

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II. METHODOLOGY
Concepts that were incorporated in the analysis of the data gathered were
identified in this section to support the objectives of the research study.
i. Data Source
This study provides a quantitative and qualitative analysis of the A’s Laundry
Shop located at Mintal, Davao City. The researchers saw a great potential to conduct a
profit maximization analysis because of its competitive advantage in terms of being the
leading and long standing laundry shop with a highly recommended quality finished
products.
Data were gathered through an interview with the owners. Start-up capital, as
well as the total revenue, net profit, total labor expenses and operating expenses, were
accessed and retrieved on a monthly basis starting January 2011 to Sept 2014. (See
Appendix)
ii. Data Analysis
To further comprehend the data collected, the researchers used different
analytical solutions, models and software such as:
Microsoft Excel
Data collected were encoded in Excel. It is an electronic program that can be
used for storing, organizing and tabulating data. It is a software that uses spreadsheet
system broken up by rows and columns allowing users to organize, format, and
calculate data with formulas (businesssdictionary.com).
Cobb-Douglas Production Function
This production function is used to identify the model of production. It is used
to understand the relationship of output to inputs. It is considered a simplified view of
the economy in which production output is determined by the amount of labor involved
and the amount of capital invested, holding other factors constant.

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Gretl (GNU Regression, Econometrics and Time-series Library)
It is a software that deals with any macroeconomic time series. It is used to
regress the data collected in order to obtain the correct model to be used.
Lingo Programming
LINGO is a comprehensive tool designed to build and solve Linear, Nonlinear
(convex & nonconvex/Global), Quadratic, Quadratically Constrained, Second Order
Cone, Stochastic, and Integer optimization models faster, easier and more efficient.
LINGO provides a completely integrated package that includes a powerful language
for expressing optimization models, a full featured environment for building and editing
problems, and a set of fast built-in solvers. (LINDOSystemsInc.). It is used to compute
for the maximum profit and the maximum amount of labor and capital.
Hessian Matrix
Hessian is a square matrix of second-order partial derivatives of a function. It
describes the local curvature of a function of many variables. It is used to check if the
function is maximizing or minimizing.
SWOT Analysis
This is used to evaluate the strengths, weaknesses, opportunities and threats,
and also to provide strategies to the firm. Through this, the internal and external factors
that are favorable and unfavorable to achieve the firm’s objective are identified.

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III. RESULTS AND DISCUSSION
i. Data Modeling
Data that were gathered (See appendix 1) were run through the software Gretl
to determine the exponents to be used in constructing the Cobb-Douglas production
function.

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The obtained coefficients for K and L were substituted as the exponents of the
production function.
= �� � �
= �− . . .
ii. Profit Maximization
Objective function: �� � = − +
= �− . . .
Constraint: . . ≥ ; ≥
The variable p denotes price per kilo, which is Php20; q for output per kilo which is
denoted by the Cobb-Douglas production function; K for capital; and L for labor.
The values of p and q are substituted to the objective function:
�� � = [�− . . .
] − +
�� � = [�− . . .
] − +
�� � = . . .
] − +
After substitution, the values of the objective function, constraint and the budget (which
is Php19605.48 – highest monthly total expenses; refer to Appendix) were then run through
Lingo for computation for the maximum profit.

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Results:
*K= 13,978.71 (pesos)
*L= 5,626.773 (pesos)
Π = 38, 712.34 (pesos)
iii. Hessian Matrix
To prove that the function is a maximum, the second-order partial and cross-
order derivatives were computed to come up with the Hessian Matrix.
First Order Derivatives
Lk (K,L)= . . . − .
]
= 3.860634093 K-0.287384 .
LL(K,L) = . . . . −
= 1.559291833 . − .

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Second-Order Derivatives:
LKK (K,L)= 3.860634093(-0.287384)K-0.287384-1
L0.287384
= -1.109484468K-1.287384
L 0.287384
LLL (K,L)= 1.559291833 (-0.71261216)K0.712616
L -1.712621
= -1.1111 K0.712616
L -1.712621
Cross-partial Derivatives:
LKL (K,L)= 3.860634093(0.287384) K - 0.287384
L -0.712616
=1.11K- 0.287384
L -0.712616
LLK (K,L)= 1.559291833(0.712616) K - 0.287384
L -0.7121616
=1.11K- 0.287384
L -0.171216
Substituting the values of K and L
*K= 13,978.71
*L= 5,626.773
Lkk (K,L)= -1.109484468K-1.287384
L 0.287384
= -6.11 x 10-5
LLL (K,L)= -1.1111K0.712616
L -1.712621
= -3.78 x 10-4
LKL (K,L)= 1.11 (13,978.71) - 0.287384
(5,626.773) -0.171216
= 0.016
LLK (K,L)= 1.11 (13,978.71) - 0.287384
(5,626.773) -0.171216
=0.016

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Hessian Matrix:
-6.11 x 10-5
0.016
0.016 -3.78 x 10-4
The matrix is negative definitive, therefore, (*K,*L) is a local maximizer.
Output function:
= �− . . .
= �− .
. .
. .
q*= 2914.989454 kilos
Average number of laborers: Total Cost (TC):
L = L* / (daily wage x labor days) TC = K* + L*
L = 5,626.773 / Php160 x 26 TC = (13,978.71 + 5,626.773)
L = 1.35 man per day Total Cost = 19605
Total Revenue (TR): Maximum Profit (π):
TR = (p) (q*) Π = TR - TC
TR = (20) (2914.989454) Π = 58299.78908 -19605
Total Revenue = 58299.78908 Maximum Profit = 38694.30608
As seen on the Appendix, the firm has exceeded its maximum profit on August 2011,
which is Php39214.28; January 2012, which is Php40427.93; and February 2012,
Php39626.65. But due to new entrants and seasonal changes, profit has not been constant. In
fact, it has been continuously decreasing in 2014. The average of the firm’s monthly profit is
Php23067.44. It is only 59.61% of the maximum profit.

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IV. SUMMARY AND CONCLUSION
A’s Laundry Shop is indeed economically stable from establishment up until now. In
fact they have get back their start-up capital (50,000.00) the next month of operation with a net
income of Php54, 704.40 right after they’ve started (See Appendix). But then, their sales and
gross income goes in a fluctuating trend with an extreme decline on months with no class.
Thus, remedial measures should be done for sales improvement and find the best way to
maximize profit.
That problem is addressed by the results of this study which suggests that A’s Laundry
Shop can attain their maximum profit in present time by inputting Php13,978.71 of capital (K*)
and Php5,626.773 of labor (L*) per month. This combination of inputs can generate an output
(*q) of 2914.989454 kilos. These values were obtained using the Lingo software. According
to the owners, the number of laborers per day is not constant and are paid daily by Php160.
There are days that there is only one laborer and the other days with two. Thus, to determine
the number of laborers to be hired per day, the amount for labor, which is Php5626.773 is
divided by 4160 (Php160 times 26 labor days). In result, A’s Laundry Shop should hire an
average of 1.35 man per day in order to attain the maximum profit. Meaning, there are days
that there must be only one laborer, and there must be two laborers on the other days. These
number of laborers were already being practiced by the firm. Thus, there’s no need to hire
additional worker. On the other hand, A’s Laundry Shop must invest on Php13, 978.71 amount
of capital. Based on the data gathered (Appendix), the firm’s lowest input in capital was on
June 2014 which is Php1, 190.00 and the highest was on March 2012, which is Php14, 805.48,
that exceeded the required capital. This implies that they must reach and/or limit their input on
the required capital every month to attain maximum profit of Php38, 694.31.

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V. RECOMMENDATION
To further analyze and give more effective recommendation, the researchers also
conducted a qualitative study on the firm through SWOT analysis.
SWOT ANALYSIS:
STRENGTHS
S1- Years in Business
Throughout the years A’s Laundry Shoppe had established a reputation and reached
stability already . Thus, students from nearby campuses became reliant patrons of the business.
S2-Quality Products
Quality check and careful inspection is done by the the owner based on its standard
checklist before it is returned to the owner. Unqualified products are sorted and are subject to
undergo the cleaning process again befor being given to costumers.
S3-On time date
Owners are buiness conscious. Thus, on time availability of finished laundries are
strictly complied for a minimum of 2 days and a maximum of 5 days in peak season.
S4-Special offers
Special requests are granted but with corresponding amount such as rush orders.
S5-Strategic Location
The business is located at the heart of barangay. Students who went out for dinners on
restos nearby, get money from pawnshop, do grocery and hang out downtown, find it easy to
drop their laundries by the shop.
S6-Home-based
It is situated at the house of the owners. Thus, extra cost for rent (which usually is the
biggest expenditure for some business) is not a problem.

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S7-Hands on owners
With the business right in front of their eyes, the owners’ attention, time and
sorroundings are mainly focused on the business. They even work hand in hand with their
employees.
S8-Minimum Requirement
The shop has a minimum-of-3-kilos rule wherein the costumers are reminded to submit
3 kilos or more of laundry. Nonetheless, if their clothings do not reach or exceed 3 kilos, they
are required to pay the price of a 3 kilo even so.
WEAKNESS
W1-Limited machineries
Available washing machines and driers can be counted barely by hands. Thus, making
operations slower specially during peak and rainy season respectively.
OPPORTUNITIES
O1-Expansion
Economic stability of the business makes it viable for expansion or extension. In fact,
there were offers asking them to branch out and extend their services to nearby communities.
O2-Academic Calendar Shift
UP Mindanao, wherein most of their student patrons study, recently undergo an
Academic Calendar shift which is an advantage to shop. It is due to the savings in electricity
in terms of drying wet clothes using driers in rainy seasons. Also, summer, which is supposedly
the lowest earning point of the shop, is now unvacated due to the students’ ongoing class on
April and May.
THREAT
T1-New Entrants
Due to the laundry service potential, new entrants are enticed to join the industry and
venture the said business. Thus, number of competitors is constantly rising and the students
has now lots of choice where to avail laundry service.

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Opportunities Threat
SWOT MATRIX O1 – Expansion T1 - New Entrants
O2 - Academic Calendar Shift
Strengths SXO Strategies SXT Strategies
(S1*S2*S3*S4*S5*S6*S7*S8*O1*O2) (S1*S4*S5*T1)
S1 - Years in business - Expand Operations - Advertising enhancement
S2 - Quality Products - Venture branching out - Branching
S3 - On time date - Further develop the business center - Self-expansion
S4 - Special Offers
S5 - Strategic Location
S6 - Home based
S7 - Hands on owners
S8 - Maximum kilo
requirement
Weakness WXO Strategies WXT Strategies
(W1*O1) (W1*T1)
- Adding more machineries - Add more machineries
W1 - Limited machineries (W2*T1)
- Operational Advancement
The researchers recommend that the best strategy to implement is to expand the
business through building branches nearby such as dormitories and boarding houses wherein
target market, like students, reside. At the same time, advancement on the procedures needs to
be done through investing in technological resources to improve their operations and gain a
large advantage over existing competitors and new entrants.
Moreover, during no class months, advertisement should be given importance
especially unto non-students. Also, they should now be open and ready to entertain vast
external orders from households and if possible to big time entities nearby.

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VI. APPENDIX
Raw Data:
Legend:
Green – highest total expenses Yellow - profit that exceeded the maximum profit
Blue – highest capital expense Violet – lowest capital expense
January – December 2011
Month Gross Revenue Quantity
Capital
Expense Labor Expense Total Expense Net Profit
January 39038 1951.9 7219.1 5294.76 12019.1 27018.9
February 40701 2035.05 8215.5 5733.7 13015.5 27685.5
March 44490 2224.5 8877.55 6025.35 13677.55 30812.45
April 20032 1001.6 4110.15 3925.18 8910.15 11121.85
May 21058 1052.9 2813.45 3353.94 7613.45 13444.55
June 37305 1865.25 8260.4 5753.48 13060.4 24244.6
July 54581 2729.05 12336.14 7548.96 17136.14 37444.86
August 55581 2779.05 11566.72 7210.01 16366.72 39214.28
September 47621 2381.05 10135.01 3200 14935.01 32685.99
October 32383 1619.15 7712.44 4300 12512.44 19870.56
November 37929 1896.45 8321.8 3600 13121.8 24807.2
December 43242 2162.1 11550.5 4800 16350.5 26891.5
January – December 2012
Month Gross Revenue Quantity
Capital
Expense Labor Expense Total Expense Net Profit
January 57296 2864.8 12068.07 7430.87 16868.07 40427.93
February 56947 2847.35 12520.35 7630.11 17320.35 39626.65
March 58266 2913.3 14805.48 8636.78 19605.48 38660.52
April 20524 1026.2 2179.03 3074.46 6979.03 13544.97
May 20699 1034.95 2145.43 3059.66 6945.43 13753.57
June 42709 2135.45 9577.47 6333.69 14377.47 28331.53
July 46150 2307.5 10868.7 6902.51 15668.7 30490.3
August 44366 2218.3 10480.98 6731.71 15280.98 29085.02
September 50021 2501.05 11056.05 6985.04 15856.05 34164.95
October 33260 1663 7594.7 5460.22 12394.7 20865.3
November 36136 1806.8 7874.68 5583.56 12674.68 23461.32
December 45395 2269.75 9671.05 6374.91 14471.05 30923.95

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January – December 2013
Month Gross Revenue Quantity
Capital
Expense Labor Expense Total Expense Net Profit
January 42418 2120.9 9456.74 6280.5 14256.74 28161.26
February 45955 2297.75 11439 7153.74 16239 29716
March 45693 2284.65 10319 6660.35 15119 30574
April 19045 952.25 4637.96 4157.69 9437.96 9607.04
May 18985 949.25 4173.47 3953.07 8973.47 10011.53
June 34325 1716.25 7725.37 5400 12525.37 21799.63
July 48465 2423.25 13085.58 8640 17885.58 30579.42
August 42395 2119.75 11322.35 7570 16122.35 26272.65
September 44700 2235 11508.63 7700 16308.63 28391.37
October 31435 1571.75 8299.77 5750 13099.77 18335.23
November 33035 1651.75 7235.87 5110 12035.87 20999.13
December 38405 1920.25 12987.32 6330 17787.32 20617.68
January – September 2014
Month Gross Revenue Quantity
Capital
Expense Labor Expense Total Expense Net Profit
January 41730 13773.65 5900 7873.65 13773.65 13773.65
February 40705 14918.82 6840 8078.82 14918.82 14918.82
March 45680 15805.34 7630 8175.34 15805.34 15805.34
April 26920 12599.54 4230 8369.54 12599.54 12599.54
May 23075 8545.13 2720 5825.13 8545.13 8545.13
June 17210 5701.09 1190 4511.09 5701.09 5701.09
July 27565 7093.13 5100 1993.13 7093.13 7093.13
August 37935 12515.9 5270 7245.9 12515.9 12515.9
September 43780 13439.18 4930 8509.18 13439.18 13439.18
Average:
Gross Revenue Quantity
Capital
Expense Labor Expense Total Expense Net Profit
38559.68889 3909.357333 8176.929111 6005.245111 13363.19089 23067.44378

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VII. REFERENCE
Government Website Phils. “Annual Survey Philippine Business and Industry (ASBPI)
and Other Service Activities 2010”. URL : http://web0.psa.gov.ph/content/, Retrieved
December 2014