A standard maximization problem in n unknowns is a linear programming problem in which we are required to maximize the objective function:
Z = c1x1 + c2x1 + . . . + cn xn
subject to constraints of the form
a11x1 + a12x2 +. . .+ a1nxn ≤ b1
a21x1 + a22x2 +. . .+ a2nxn ≤ b2
. . .
am1x1 + am2x2 +. . .+ amn xn ≤ bm
and further restriction of the form x1 ≥ 0, x2 ≥ 0 , . . . , xn ≥ 0
Note that the inequality here must be a " ≤ " and not "=" or "≥"

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first a convert all the constraints and the objective functions in to a linear equations .
then it become x1 + x2 = 6
x1=3
x2=3
2×1+3×2 = 3
After substitution in equations to find the points
(3,3) is the point pf interaction of x1=3 and x2=3
and the corner points in the feasible region is (3,0) , (5,0) .

then substitution in the objective function z = 5×1 + 3×2 .

the maximum value at x=5 and x2=0
maximun value is 25

the minimum value at x1=3 and x2=0 .
minimum value is 15

i’am i right ??
could any one guide me .

first a convert all the constraints and the objective functions in to a linear equations .
then it become x1 + x2 = 6
x1=3
x2=3
2x1+3x2 = 3
After substitution in equations to find the points
(3,3) is the point pf interaction of x1=3 and x2=3
and the corner points in the feasible region is (3,0) , (5,0) .
then substitution in the objective function z = 5x1 + 3x2 .
the maximum value at x=5 and x2=0
maximun value is 25
the minimum value at x1=3 and x2=0 .
minimum value is 15
i'am i right ??
could any one guide me .

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could you just help me in these question because i want to make sure about my answer and understanding .
Consider the graphical representation of the following LPP
Maximize
Z = 5x1
+ 3 x2
Subject to x1 +
x2 6,
x1 3
x2
3
2x1 + 3 x2
3
x1 0 , x2 0.
Answer the following questions:
(a) In each of the following cases indicate if the
solution space ( the feasible region) has one point, infinite number of points, or no points.
1.
The constraints are
as given above.
2.
The constraint x1
+ x2 6
is changed to x1 + x2 5.
3.
The constraint x1
+ x2 6
is changed to x1 + x2 7.
(b) For each case in (a) , determine the number of feasible extreme points, if any.
(c) For
the cases in (a) in which a feasible solution
exists , determine the maximum values of Z .
(d) Answer part (c) for minimize Z.

That is the statement of a practice problem. In order to help, we need to see the work that you have done. We can then point to errors or clarify your understanding. But we can't do the work for you. For example, show your objective row values first. -- Tom

first a convert all the constraints and the objective functions in to a linear equations .
then it become x1 + x2 = 6
x1=3
x2=3
2x1+3x2 = 3
After substitution in equations to find the points
(3,3) is the point pf interaction of x1=3 and x2=3
and the corner points in the feasible region is (3,0) , (5,0) .
then substitution in the objective function z = 5x1 + 3x2 .
the maximum value at x=5 and x2=0
maximun value is 25
the minimum value at x1=3 and x2=0 .
minimum value is 15
i'am i right ??
could any one guide me .

You don't show your matrices, so it's hard to tell how you got your results. But it looks like you're doing okay so far.
Let's see:
Z = 5X1 + 3X2
With constraints:
X1 + X2 ≤ 6
X1 ≥ 3
X2 ≥ 3
2X1 + 3X2 ≥ 3
Additional constraints (that are true but logically unnecessary):
X1 ≥ 0 ; X2 ≥ 0
Personally, I find the first three constraints a little odd. Both X1 and X2 can only equal 3. There are no other values that can possibly satisfy:
X1 + X2 ≤ 6
Where did you get the problem?
Tom

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