Equality Dual Constraint

Write the dual for each of the following primal problems:

(a) Maximize z = 66×1 – 22×2

subject to

-x1 + x2 smaller than or equal -2

2×1 + 3×2 smaller than or equal 5

x1, x2 greater than or equal 0

(b) Minimize z = 6×1 + 3×2

subject to

6×1 – 3×2 + x3 greater than or equal 25

3×1 + 4×2 + x3 greater than or equal 55

x1, x2, x3 greater than or equal 0

(c) Maximize z = x1 + x2

subject to

2×1 + x2 = 5

3×1 – x2 = 6

x1, x2 unrestricted

4-6. True or False?

(a) The dual of the dual problem yields the original primal.

(b) If the primal constraint is originally in equation form, the corresponding dual

variable is necessarily unrestricted.

(c) If the primal constraint is of the type …, the corresponding dual variable will

be nonnegative (nonpositive) if the primal objective is maximization

(minimization).

(d) If the primal constraint is of the type Ú, the corresponding dual variable will

be nonnegative (nonpositive) if the primal objective is minimization (maximization).

(e) An unrestricted primal variable will result in an equality dual constraint.