Question

Convert the following formulation to a 2 variable problem so that it can be solved graphically (HINT: Eliminate one of the variables – say X3...). Sketch the feasible region and compute the coordinates of its extreme points.

5X₁ + X₃$\geq$ 17

2X₁ + 1.5X₂ + X₃$\geq$ 14

.5X₁ + 2X₂ + X₃$\geq$​​​​​​​ 10

X_{1 ,} X₂ , X₃$\geq$​​​​​​​ 0

Answer 1

Given J 544237,17 284 41.582 tag7,14 574 +222 +23710 24,92,93 20 Put 23 20 we get in ② 547,17 24 + 3 x 2 roog?14 1/2 4 + 2% 710 =) 5 7,17 434 43427,28 x +412 7,20 04, 2270 . 21,227,0 4+42.= 20 862E+ het ZTEIS Here Shaded region is feasible reasi region of this problem, which is unbounded

Here A, B and C are extreme point Coordinate of is (2010) to To find A, B we solve the ean given eque (*) consider as equal & for Point Awe to 44 = Solve ears for Point B we Solve the eah & 488 +32 =28 | 441322=28 4x17 / + 322 =28 If 34 74m2 =20 3) 322 = 28- 68 434+372 =28 y 24 +16*2 = 80 -1372 = -52 24, 92-24 84 24 x=20-4x4 . Coordinate of A = (325) .. Coordinate of B- (514) Y = 28x9-68