Question

5x y>_10 x y<_6 x 4y>_12 x>_0 y>_0 minimum for c=10,000x + 20,000y

Answer 1

We are given inequalities : 5x+y=>10

x+y<=6

x+4y=>12

x=>0

y=>0 .

Let us graph it first and the find the coordinate of the vertices of feasible region.

Coordinates of the feasible region are (1,5) , (1.474, 2.632) and (4,2).

Now, we need to plug those cordinates (1,5) , (1.474, 2.632) and (4,2) in the given function c=10,000x + 20,000y.

Let us plug those points one by one.

For (1,5)

c=10,000x + 20,000y = 10,000(1)+ 20,000(5)= 10,000+ 100,000 = 110,000.

For (1.474, 2.632)

C = 10,000(1.474)+ 20,000(2.632) = 67,380.

For (4,2)

C = 10,000(4)+ 20,000(2) = 80,000.

We got the minimum value 67,380 for (1.474, 2.632) coordinate.

Therefore, minimum for given function C=10,000x + 20,000y is 67,380.