Minimize Z 5x1 6x2 Subject to x1 2x2 10 2x1 3x2 0 x2 0

Minimize Z = 5x1+ 6x2

Subject to: x1 + 2x2 >= 10

2x1 - 3x2 <= 6

x1 + x2 = 6

x1 >= 0

x2 >= 0

a) Find the dual of the primal

b) show that the dual of the dual is the primal.

Solution

Let x1 be the number of units of exterior paint x2 be the number of units of interior paint Maximize Z = 5x1 + 4x2 Subject to 6x1 + 4x2 24 x1 + 2x2 6 x2 – x1 1 x2 2 x10, x2 0 b) The maximum daily demand for exterior paint is atmost 2.5 tons x1 2.5 c) Daily demand for interior paint is atleast 2 tons x2 2 d) Daily demand for interior paint is exactly 1 ton higher than that for exterior paint. x2 > x1 + 1