Linear Objective Function

Introduction to Linear objective function:

A linear objective function is definite as an algebraic equation in which all expression is also a stable or the product of a stable and a single variable. Linear objective functions can contain one or more than one variables. Linear objective function is happening among great dependability in applied mathematics. A linear function is one whose diagram is a straight line.

Format of Linear Equations and Objective Function:

Objective function:

A function connected by an optimization problem which determines how good quality a solution is, for instance, the total cost of limits in a solution to a travelling salesman problem.

Linear equations:

A familiar type of linear equation in the two variables x and y is,

y =mx+b.

Here m and b is constants. Now the expression linear is derivative from a graphical line of diagram. To facilitate is straight line is happening at a graph.

General form:

Ax+By+C=0.

Where, A and B both not equal to zero.

Standard form:

Ax+By=C.

Where, A, B, and C are integers.

Slopeintercept form:

y=mx+b.

Where m indicates the slope of line and b indicates the y intercept.

Linear functions:

A linear function is definite as a function whose chart consists of sectors of one straight line through its domain.

We know how to found the linear function and it acquires value f (a) at a and f (b) at b during the following formula:

f(x)=f(a) (x-b)/(a-b) + f(b) (x-a)/(b-a).

Because the first term is Zero (0) when x is b and is f (a) when x is a, while the second term is Zero (0) when x is a and is f(b) when x is b.

Examples of Linear Objective Function:

Example 1:

Solve 3[5m - (6 -8m)] = m - 16.

Solution:

solve left hand side

=> 3[5m-(6-8m)]

Here first solving the inside term.

=> 3(5m-6+8m) and then,

=> 3(13m-6)

=> 39m -18

Now compare with right hand side.

=>39m- 18= m-16

39m-m = 18-16

38m = 2

m = 19.

Therefore m = 19.

The Answer: m = 19.

Example 2:

Solve 4(6m - 1) = 4(m + 6).

Solution:

4(6m - 1) = 4(m + 6)

24m - 4 = 4m + 24

24m - 4m = 24 + 4

20m = 28

m = 28/20

m = 7/5.

The Answer: m = 1.4.

by: johnharmer

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