The document describes using linear programming to maximize profit for two products at Saudi Dairy and Foodstuff Company. Data was collected from the company on production, sales, resources and constraints. A linear programming model was developed and solved using LINGO 18.0 software. The optimal solution was found to be producing 15.52741 units of the first product and 1017 units of the second product, yielding maximum profit of 524.2614 Saudi Riyals.

1. Using Linear programingmethod to
maximize the profit of tow products
at saudi dairy and foodstuff Company
(sadafco)
Prepared by:
Yahya jamumi
Mohand abdul salam abdul jabbar
Ahmed al subhi
Abdullah bahashwan
Talal hosawi
Supervised by:
Eng/Wael Alhajjaji

2. OUTLINE
1- Abstract
2- Introduction
3- Literature Review
4- Methodology
5- Solving and Result
6- Conclusion
7- Recommendation

3. ABSTRACT
This paper aims for profit optimization of Saudia Dairy & Foodstuff Company (sadafco)
and cosmetics factory located in Jeddah (Saudi Arabia) using linear programming model.
The first step comprises data generation by visiting that firm and collecting the
information needed from the company staff both executive and staff to determine the
production, sales, resources and limitations (constraints).
It was established that the decisions are undertaken by experienced people without
usage of quantitive people and quantitive method.
A linear programming model for the company is developed for profit optimization. The
model equations with adequate restrains taking into account manufacturing limitations
are solved using LINGO 18.0 software. Finally, some conclusive observations have been
drawn and recommendations have been suggested.

4. Background
 Operations research
is a quantitative approach that solves problems, using
a number of mathematical techniques.
 It is helpful to use operations research
• when you're trying to make decisions, but the
conditions are uncertain,
• and when differing objectives are in conflict with
each other.

7. Problem statement
Linear programing is a set of techniques and methods inferred
from mathematics and other science, but it has well proved to be
capable of solving problems such as production planning,
allocating resources, inventory control. Those managers who care
about the best outcomes for their decisions cannot be indifferent
to this.
This technique was applied in SADAFCO ICE CREAM FIRM by taking
the required information to maximize the profit of this firm.
However, this research is set a good case study to optimize the
outcome of this company

8. The Project Objectives
The main objectives of this research are :
 To formulate a linear programing model that would suggest a viable product-
mix to ensure optimum profit for company.
 To highlight the peculiarities of using linear programing technique for the
company and prove that despite obstacles, the application of the technique in
determining the product-mix of the company would be more profitable then
otherwise.
 To know about the constraints of the company regarding cost, resources and
labor hours.

9. LITERATURE REVIEW

10. A Case Study of Ethiopian Chemical
Company
Abstract:
This paper aims for profit optimization of an Ethiopian chemical company located in Adama (Ethiopia) using linear
programming model. Particularly, our present study brings out clearly the necessity of using quantitative
techniques for utilization in Ethiopian company; a factory situated within Adama about 90 kms. from Addis Ababa
(Capital of Ethiopia). The first step comprises data generation. A questionnaire is prepared and circulated
amongst company staff both executive and technical to determine the production, sales and profit during a few
months of 2014. The profits varied considerably owing to subjective approach. It was established that the
decisions are undertaken by experienced people without use of Quantitative people and quantitative method.
Whole approach applied here is seemingly subjective. A theoretical perspective undertaken for the present study
is review of various different applications of linear programming. The characteristics of base assumptions of linear
programming and its advantages and disadvantages towards establishing its need for optimization are briefly
outlined in terms of its application to the factory. Survey data is analyzed to determine the style of decision
making and the problem is defined. An objective function is created in terms of decision variables of production,
sales and profit over a period of time using the quantitatively available data of these parameters.
A linear programming model for company is developed for profit optimization. The model equations with
adequate restraints taking into account manufacturing limitations are solved using MS-Excel solver. Finally, some
conclusive observations have been drawn and recommendations have been suggested.

11. case study solution
The constraints of the company are expressed as follows:
Maximize Z max = 3,760.66x1 + 4,604.58x2,
subject to:
0.45x1 + 2.15x2≤24 hrs. (machine hrs. on reaction),
0.2x1 +2.15x2≤24 hrs. (machine hrs. on filtration),
0.1x1 + 2.15x2≤24 hrs. (machine hrs. on evaporation),
x1≤20 tons (demand for aluminum sulphate per day),
x2≤51.5 (sulphuric acid produced per day),
x1, x2≥0 (non-negativity).

12. case study solution
Result Analysis
The optimal feasible solution is x1= 20 tons of aluminum sulphate per day,
x2 = 6.98 tons of sulphuric acid per day, s1=0, s2=5 hrs., s3=7 hrs., s4=0, s5=44.52
tons, yielding the maximum profit Zmax= Birr 107,353.17 per day.
Company produces 20tons of aluminum sulphate per day(20tons/day×300working days = 6,000
tons/annum) and 6.98 tons of sulphurc acid per day (6.98tons/day×300 working days = 2,094tons/annum)
in order to get a maximum daily profit of Birr107,353.17 per day (Birr107,353.17 per day ×300working days
=Birr32,205,951per annum).
In this way, the company is left with an idle filtration and evaporation times of 5 and 7 hours per day and
unutilized demand for sulphuric acid of 44.52tons per day but the demand for aluminum sulphate is fully
utilized.

13. METHODOLOGY

14. Background of visit
During the team's first meetings, a factory was
selected to undergo our case study sadafco factory
in the second industrial city in Jeddah was selected
due to accessibility and the will to share sensitive
information which included profit margin, operation
cost and facility planning and management in the
shop floor.

15. The data will be later handed over to the factory
manager to apply the necessary actions in order to
improve Factory operation and profitability

16. In side factory at product lines

17. Linear Programing (LP):
Linear programming is the most common method of
decision making .
Linear programming plays an important role in addressing
the problems that lead to maximizing or minimizing the role
of the goals in a given field, based on the constraints
imposed on a number of important variables, and can be
described as a very important method to support the decision
maker and enable him to make the right decision based on
Scientific methods.

18.  The data collection procedure was quantitative in nature and relied on
face-to-face interviews with members of the management and line
supervisors in accordance with existing records and merely amended to
finalize the concepts relevant to the resources held and consumed and
the production volume of each product in the case company.
 The relevant information on the amount of resources used per unit of
each product during the day is summarized in Table

19. Resources needed per unit of product
Products SAUDIA BABOO CONES SAUDIA BABOO PUSHUPS NOT EXCEED
water 681.4 874.15 900000
Sugar 175.1 kg 219 kg 250000
Flour 40 kg 0 45000
salt 13.3 kg 0 1000
Soy lecithin powder 0.08 kg 0 1000
Starch 0.6 kg 0 1000
AMF 110 kg 0 120000
SMP 29 kg 0 3000
Cremodan 8.2 kg 0 900
Coco powder 30 kg 0 6000
Food Stabilizer 0 3.6 kg 4000
Rosemary liquid 0 11.7 kg 12000
Rosemary powder 0 0.8 kg 1000
Red powder 0 0.84 kg 20000

20. Quantity of each product
Products Quantity (per day)
SAUDIA BABOO CONES 1000
SAUDIA BABOO PUSHUPS 1800

21. Mathematical modeling
Decision variables
The information collected from the case company in addition
to the sales and other operating data was analyzed to provide
estimates for LPP model parameters. To set up the model, the
first level decision variables on the volume of products to be
produced were set.
X1 = BABOO CONES
X2 = BABOO PUSHUP

22. Mathematical modelingObjective function:
is a linear function of the decision variables representing the objective of the
manager/decision maker. [9]
Max z = 1 X1 + 0.5 X2
Constraints
are the linear equations or inequalities arising out of practical limitations. [10]
681.4 X₁ + 874.15 X₂ +S1 =900000
1750.1 X₁ + 219 X2 +S2=250000
40 X₁ +S3=4500
13.3 X₁ +S4=1000
0.08 X₁ +S5=1000
0.6 X₁ +S6=1000
110 X₁ +S7=120000
29 X₁ +S8=3000
8.2 X₁ +S9=900
30 X₁ +S10=6000
3.6 X₂ +S11=4000
11.7 X₂ +S12=12000
0.8 X₂ +S13=1000
0.84 X₂ +S14=20000)

23. SOLVING MODEL AND RESULTS

24. Simplex method of linear programing
The Simplex Method provides a systematic search
so that the objective function increases in the
cases of maximization progressively until the basic
feasible solution has been identified where the
objective function is maximized

25. Algorithm of data collection
Objective function:
Maximize Z = 1 X1 + 0.5 X2
Subject to:
681.4 X₁ + 874.15 X₂ =900000
1750.1 X₁ + 219 X2 =250000
40 X₁ =4500
13.3 X₁ =1000
0.08 X₁ =1000
0.6 X₁ =1000
110 X₁ =120000
29 X₁ =3000
8.2 X₁ =900
30 X₁ =6000
3.6 X₂ =4000
11.7 X₂ =12000
0.8 X₂ =1000
0.84 X₂ =20000
X₁ , X₂>= 0

26. Implementation
Objective function:
Maximize Z = 1 X1 + 0.5 X2
Subject to:
681.4 X₁ + 874.15 X₂ +S1 =900000
1750.1 X₁ + 219 X2 +S2=250000
40 X₁ +S3=4500
13.3 X₁ +S4=1000
0.08 X₁ +S5=1000
0.6 X₁ +S6=1000
110 X₁ +S7=120000
29 X₁ +S8=3000
8.2 X₁ +S9=900
30 X₁ +S10=6000
3.6 X₂ +S11=4000
11.7 X₂ +S12=12000
0.8 X₂ +S13=1000
0.84 X₂ +S14=20000
X₁ , X₂+S1+S2+S3+S4+S5+S6+S7+S8+S9+S10+S11+S12+S13+S14>= 0

27. By using LINGO 18.0 program application
Better Performance on
Linear Models with Improved Simplex Solvers.
• Enhancements to the Simplex solvers boost speed on linear models.
• Models solve an average of 18% faster using primal simplex and
15% faster for dual simplex.

28. By using LINGO 18.0 program application
By adding algorithm inside the LINGO

29. By using LINGO 18.0 program application
Profit Card in shown

30. Profit Solution

32. Optimal solution
Z=524.2614 SR
X1 = 15.52741 piece
X2 = 1017.468 piece
S1 = 0 S: slack
S2 = 0
S3 =3878.904 (water)
S4 = 793.4855 ( sugar)
S₅ =998.7578 (flower)
S₆ =990.6836 (salt)
S₇ =118292.0 ( soy lecithin powder)
S₈ =2549.705 (starch)
S₉ =772.6753 (AMF)
S₁₀ =5534.178 (SMP)
S₁₁ =337.1153 (cremodan)
S₁₂ =95.62476 ( coco powder)
S₁₃ =186.0256 (food stabilizer)
S₁₄ =19145.33 (rosemary liquid)

33. paragraph
Profitability before and after
afterbefore
524.2614350.3433
The difference between profitability
173.9181

34. Recommendation
 Through these final results we found the factory
produces tow products and each product has its
profitability.
 if we reduce the production of the first product and
increase the production of the second product this
will be profitable .
 We well as by studying the case we found surplus in
raw materials.

35. Thank you for listening
any questions