Wednesday, January 25, 2023

FORM FOUR MATHEMATICS NOTES TOPIC 8:LINEAR PROGRAMMING

FORM FOUR MATHEMATICS NOTES TOPIC 8:LINEAR PROGRAMMING

FORM FOUR MATHEMATICS NOTES TOPIC 8:LINEAR PROGRAMMING
Wednesday, January 25, 2023
linear programming is a method of optimising operations with some constraints. The main objective of linear programming is to maximize or minimize the numerical value. It consists of linear functions which are subjected to the constraints in the form of linear equations or in the form of inequalities

FORM FOUR MATHEMATICS NOTES TOPIC 8:LINEAR PROGRAMMING




FORM FOUR MATHEMATICS NOTES TOPIC 8:LINEAR PROGRAMMING


Simultaneous Equations

Simultaneous Equation from Word Problems
Form simultaneous equation from word problems

LINEAR PROGRAMMING

Linear programming – is a branch of mathematics which deals with either minimizing the cost or maximizing the profit.
  • It gives the best way of utilizing the scarce resources available.
  • It is so called because it only involves equations and inequalities which are linear.
Simultaneous Equation

One
of the methods used in solving linear simultaneous equations is a
graphical method. Two linear simultaneous equations in two unknowns can
be graphically solved by passing through the following procedures.
  1. Draw
    the two lines which represent the two equations on the xy – plane this
    is done by deter mining at least two points through which each line
    passes, the intercept are commonly used
  2. Determine the point of intersection of the two lines. This point of intersection is the solution to the system of equations.
FACT:
  • If two straight lines are not parallel then they meet at only one point:
  • In case the lines do not meet, there is no solution to the corresponding system of simultaneous equations.
Example 1
Graphically solve the following system of simultaneous equations.
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
Example 2
Find the solution to the following system of simultaneous equations by graphical method.
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
Solving Simultaneous Equations Graphically
Solve simultaneous equations graphically
Example 3
Solve the following simultaneous equations graphically and check your solution by a non-graphical method:
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
Example 4
Find the solution to the following system of simultaneous equations by graphical method.
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
Exercise 1
Find the solution to the following systems of simultaneous equations graphically.
FORM FOUR MATHEMATICS NOTES TOPIC 8: LINEAR PROGRAMMING
Try:

Ali paid 34 shillings for 10 oranges and 35 mangoes. Moshi went to the
same market and paid 24 shillings for 16 oranges and 18 mangoes. What
was the price for a mango and for an orange?

FORM FOUR MATHEMATICS NOTES TOPIC 8:LINEAR PROGRAMMING
4/ 5
Oleh

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