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  • Solve the following linear programming problem graphically : Maximize subject to the constraints <img alt="4x+6y\leq 240" src="https

Solve the following linear programming problem graphically :
Maximize Z= 7x+10y
subject to the constraints
4x+6y\leq 240
6x+3y\leq 240
x\geq 10
x\geq 0,y\geq 0

 

 

 

 
 
 
 
 

Answers (1)

we have , Maximize Z= 7x+10y
subject to constraints : 4x+6y\leq 240
                                     6x+3y\leq 240
                                     x\geq 10 ,x\geq 0,y\geq 0
converting the given inequalties into equations, we obtain the following equations:
4x+6y= 240   

x 0 60
y 40 0

6x+3y= 240

x 0 40
y 80 0

x = 10 is a line parallel to y axis
Corner points                                 value of Z = 7x+10y
D(40,0)                                        7(40)+10(0) = 280
E(30,20)                                      7(30)+10(20) = 410
F(10,200/6)                                 7(10)+10(200/6) = 403.33
G(10,0)                                        7(10)+10(0) = 70
Plotting there points on the graph we get the shaded feasible region ie DEFQD.

\frac{Scale xy axis}{0\cdot 5cm= 10\, units}\rightarrow clearly the maximum value of z is 410 at (30,20)

Posted by

Ravindra Pindel

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