## Standard Maximization Problem in linear programming

135 pts.
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Maximization Problem
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 .

## Discuss This Question: 9 Replies

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• Interesting, but do you have a problem? -- Tom
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• i didn't get it very well . could any one explain it to me please
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• thanks no need now i understood what i missed . =)
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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.
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• here is more clear picture of the question http://www.4shared.com/photo/kYVHM_QB/Screen_shot_2012-09-29_at_8172.html