265+353=410124+312=721410+204=1676132+230=1021211+101=?????
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<h2>Answer:</h2>
- The optimal solution to the given linear programming problem exist at (100,50)
- and the optimal solution is: 5A+5B= 750
We are given a system of linear programming problem as follows:
Max 5A + 5B
s.t. A ≤ 100---------------(1)
B ≤ 80-------------(2)
2A+4B ≤400-------------(3)
which is given by:
A+2B ≤ 200
and A,B≥0
This means that the solution to this LPP will lie in the first quadrant.
( Since, both the variables A and B are greater than or equal to zero)
Now, we consider that A is represented by the x axis and B by y-axis.
We know that the optimal solution always exist at the boundary point.
Hence, by plotting these inequalities in the graph we get the boundary points as:
(0,0) , (0,80) , (100,0) , (100,50) and (40,80)
Now, we will check at which boundary point the optimal function is maximized .
Point Value of optimal function( 5A+5B)
(0,0) 0
(0,80) 400
(100,0) 500
(100,50) 750
(40,80) 600
The maximum value is obtained at (100,50).
and the value of the optimal solution is: 750
(5.75,0)
Let A be (x1,y1) , B be (x2,y2) , P be (x,y) and the ratio be m:n
Formula is,
x=(x2*m+x1*n)/(m+n)
y=(y2*m+y1*n)/(m+n)
