A primal maximization problem is given. Form the dual minimization problem.
Maximize subject to

A)Minimize Subject
B)Minimize Subject
C)Minimize Subject
D)Minimize Subject
E)Minimize Subject

Question

A primal maximization problem is given. Form the dual minimization problem. ​
Maximize  subject to
​  ​
A)​Minimize Subject ​ 
B)​Minimize Subject ​ 
C)​Minimize Subject ​ 
D)​Minimize Subject ​ 
E)​Minimize Subject

Quizplus · Accepted Answer

The primal problem is a maximization problem. To form the dual, we must convert this into a minimization problem. The objective function and the constraint set must also be rearranged.

The given primal problem is: 
Maximize 11eb0d3b_9809_e9cd_9790_976838431ead_TB1243_11 subject to
​11eb0d3b_980a_10de_9790_93260feff63d_TB1243_00

To convert this into a minimization problem, we take the negative of the objective function: 
Minimize -11eb0d3b_9809_e9cd_9790_976838431ead_TB1243_11

The constraint set can be expressed as: 
11eb0d3b_980a_10de_9790_93260feff63d_TB1243_00 <= 0

Now, we can form the dual problem. Using the standard steps, we can write the dual as:

Maximize y 
Subject to: 
y11eb0d3b_980a_10de_9790_93260feff63d_TB1243_00 <= -11eb0d3b_9809_e9cd_9790_976838431ead_TB1243_11

The coefficient of y in the constraint is the negative of the primal objective coefficient.
So, option B is the correct answer where the objective is minimized and the constraint is y11eb0d3b_980a_10e2_9790_35ca9f8c5364_TB1243_00 >= 11eb0d3b_980a_10e1_9790_a588da9b2fee_TB1243_00

A Primal Maximization Problem Is Given