LPP Formulation

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302-DECISION SCIENCE
Unit No.1. LPP
1.2 Formulation of LPP
Model
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Professor & Head Dept. of MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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LINEAR PROGRAMING PROBLEM
 At the End of the Session Student will be able to
formulate-
A. LPP Model

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Example
Two products: Chairs and Tables
Decision: How many of each to make this month?
Objective: Maximize profit

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Data
Tables
(per table)
Chairs
(per chair) Hours
AvailableProfit
Contribution
Rs. 7 Rs. 5
Carpentry 3 hrs 4 hrs 2400
Painting 2 hrs 1 hr 1000
Other Limitations:
• Make no more than 450 chairs
• Make at least 100 tables

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Decision Variables:
x = Num. of tables to make
y = Num. of chairs to make
Objective Function: Maximize Profit
Maximize Z = 7 x + 5 y
Solution

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Constraints
Have 2400 hours of carpentry time available
3x + 4y < 2400 (hours)
Have 1000 hours of painting time available
2x + 1y < 1000 (hours)

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More Constraints
Make at least 100 tables
x > 100
Make no more than 450 chairs
y < 450
Non negativity:
Cannot make a negative number of chairs or
tables
x > 0
y > 0

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LPP Model
Maximize Z = 7x + 5y – Objective Function
Subject to the constraints:
3x + 4y < 2400
2x + 1y < 1000
x > 100
y < 450
x, y > 0 - Non Negativity Condition

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General Formulation of LPP
Max/min z = c1x1 + c2x2 + ... + cnxn
subject to: a11x1 + a12x2 + ... + a1nxn (≤, =, ≥) b1
a21x1 + a22x2 + ... + a2nxn (≤, =, ≥) b2
:
am1x1 + am2x2 + ... + amnxn (≤, =, ≥) bm
x1 ≥ 0, x2 ≥ 0,…….xj ≥ 0,……., xn ≥ 0.
xj = decision variables
bi = constraint levels
cj = objective function coefficients
aij = constraint coefficients

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EXERCISE
Download any 05 examples of LPP
Model.

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For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in

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Thank You