1.7. Converting Min LPP to Max LPP and Conversely.
Each Min LPP can be converted to a Max LPP and conversely, each Max LPP can
be converted to a Min LPP.
Example 7. Consider DA LPP:
min z = 50x1 + 100x2
7x1 + 2x2 28
2x1 + 12x2 24
x1 0, x2 0 .
In this teaching material we give a brief description about Linear
Programming Problem by using a concrete example: Giapettos Woodcarving, Inc. that manufactures two types of wooden toys. We explain
all basic features of a given LP by using Giapettos Wood
Problem 1. Leather Limited manufactures 2 types of belts: a deluxe model and a
regular model. Each type requires 1 sq yd of leather. A regular belt requires 1 hour of
labor and a deluxe belt requires 2 hours. Each week 40 sq yd of leather and
Problem 1. Farmer Jane owns 45 acres of land. She is going to plant wheat and
corn. Each acre planted with wheat yields $200 prot; each with corn yields $300
prot. The labor and fertilizer used for each acre are given in the next table:
Problem 1. By using the Simplex Method, show that the given LPP is unbounded:
min z = 2x1 3x2 + x3 + 12x4
2x1 + 9x2 x3 9x4 0
x1 3x2 + x3 + 6x4 0
x1 0, x2 0, x3 0, x4 0 .
Problem 2. By using the Simplex Method show that the LPP
max z = x1
Direction of Unboundedness for an Unbounded Feasible Region.
Representation of the Points in a Feasible Region (the Feasible Solutions)
by the Extreme (Corner) Points of the Feasible Regon and a Direction of
Unboundedness of the FR.
Proof of the Extreme P
Problem 1. Farmer Jane has 45 acres of land. She is going to plant each acre of her land with
wheat and corn. Each acre planted with wheat yields 200$ prot and needs 3 workers and 2 tons of
fertilizer. Each acre planted with corn yields 300$
Linear Algebra Method to Solve LPP by using the Extreme Point Theorem
Canonical Form of a Linear Programming Problem.
Basic Solutions (BS) and Basic Feasible Solutions (BFS) of a Canonical
LPP. Basic and Non-basic Variables of a BFS.
Algebraic Computing o
How to Spot Unbounded LPP by the Simplex Method?
Let us remind what is unbounded LPP.
Unbounded Max LPP. If for a given Max LPP there exist points in the FR (feasible solutions) for which the objective function assumes arbitrary large values then
we say t
Simplex Algorithm to Solve MAX and MIN Linear Programming Problems
In this Course rst, we discussed how to solve Graphically two-variable and threevariable linear programming problems. However, most real-life LPPs have many
decision variables and
Problem 1. An auto company manufactures cars and trucks. Each vehicle must be
processed in the paint shop and in the body assembly shop.
If the paint shop were painting only trucks, then 40 trucks per day could be painted.
If the paint shop w