1) Mathematical models are representations of real-world problems or objects using mathematical concepts and language. They help simplify and solve real-life problems. 2) The process of developing a mathematical model involves finding a real-world problem, formulating hypotheses, applying mathematical knowledge to reach conclusions, and comparing predictions to real data. 3) Advantages of mathematical models include solving real-world problems, aiding decision making, enabling predictions, preserving knowledge, and optimization.

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2. BUSINESS
INTELLIGENCE
Mathematical Models
Mrs. Megha Sharma
MSc Computer Science. BEd.

3. Models:
Physical representation of an object, that shows, what it looks like or how it works.

4. Mathematical Model
“Mathematical representation of physical situation”.
(Mason & Davis,1991)
Understanding, simplifying and solving a real life problem.
(Cross & Moscardini,1985; Bassanezi,1994)
Applying mathematics which is “useful to society”.
(Yanagimoto,2005)

5. The instrument used to represent and solving real world
problems is called mathematical models. They help us to
understand how the real world works.
Every mathematical model requires a set of inputs and
mathematical functions to generate an output.
Output
Mathematical
Functions
Input

6. The Process for developing a Mathematical Model
Find a real world Problem
Establishing Hypothesis
Apply mathematical
knowledge to reach
conclusion
Compare data obtained as
prediction with real data
If the data are different
the process is restarted

7. Advantages Of Mathematical Model
Solving real world problems
Decision Making
Making Predictions.
Preservation of Knowledge
Optimizing

8. Problem Statement
A firm produces two products A and B. For producing each unit of product A, 12 Kg of Raw
material and 16 labor hours are required. While, for the production of each unit of product
B, 16 kg of raw material and 8 labor hours is required. The total availability of raw material
and labor hours is 100 Kg and 80 Hours respectively (per week). The unit price of Product
A is Rs 20 and of product, B is Rs 25.
Suppose x1 and x2 are units produced per week of product A and B respectively.
Thus the linear programming problem will be.
Maximize Z = 20x1+ 25x2 (profit)
Subject to:
12x1 + 16x2 ≤ 100 (raw material constraint)
16x1 + 8x2 ≤ 80 (labor hours constraint)
x1, x2 ≥ 0 (Non-negativity restriction)

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