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+1 vote
1.9k views
in Linear Programming by (3.3k points)
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Consider the linear programming problem: Minimise Z = 4x + 4y Subject to x + 2y < 8; 3x + 2y < 12x, y < 0 

(a) Mark its feasible region. 

(b) Find the comer points of the feasible region. 

(c) Find the corner at which Z attains its minimum.

1 Answer

+1 vote
by (4.0k points)
selected by
 
Best answer

(a) x + 2y = 8,

x

0

8

Y

4

0

3x + 12y = 12

x

0

4

Y

6

0

(b) 

The comer points are 0(0, 0), A(4, 0), B(2, 3), C(0, 4)
(c) 

Corner points

Z = -3x + 4y

O(0,0)

Z = 0 + 0 = 0

A(4,0)

Z = -12 + 0 = -12

B(2,3)

Z = -6 + 12 = 6

C(0,4) Z = 0 + 16 = 16
Z attains minimum at (4, 0).
 

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