Constraints are : x >= 0, y >= 0, x + 2y <= 1500,5x + 2y <= 3500
1) x> = 0; y >= 0 represents first quadrant i.e Q1.
2)Draw a line x + 2y =1500
|
x |
0 |
1500 |
|
y |
750 |
0 |
|
(x,y) |
(0,750) |
(1500,0) |
3) plot above points on graph sheet and draw a line.
4)substitute (0,0) in inequation x+ 2y <= 1500
you get 0 <= 1500 ( it is true)
therefore (0.0) lies x+ 2y <= 1500 region.shade the region.
5)Draw a line 5x + 2y = 3500.
|
x |
0 |
700 |
|
y |
1750 |
0 |
|
(x,y) |
(0,1750) |
(700,0) |
plot above points on the graph and draw a line passing through them
6)substitute (0,0) in inequation 5x + 2y <= 3500
you get 0 <= 3500 ( it is true ) therefore
(0,0) lies 5x + 2y < = 3500 region. shade that region.
7) x + 2y = 1500 and 5x + 2y = 3500 lines intersect at (500,500) from graph.
8) required region is bounded by the points (0,0),(700,0)
(500,500),(0,750).
|
point |
z=50x+70y |
value |
|
(0,0) |
z=50*0+70*0 |
0 |
|
(700,0) |
z=50*700+70*0 |
35000 |
|
(500,500) |
z=50*500+70*500 |
60000 |
|
(0,750) |
z=50*0+70*750 |
52500 |
therfore z is minimum at (0,0) and maximum at (500,500)