# Linear programming - problem

• December 9th 2009, 09:35 PM
dhammikai
Linear programming - problem
Hi please give me a help to find out the answer for the following linear programing question

There are two products x1 and x2 manufactured on two machines M1 and M2.
Product x1 requires 3 hours on machine M1 and half and hour on machine M2. Product
x2 requires two hours on machine M1 and one hour on machine M2. Total available
capacity on machine M1 is six hours and that on machine M2 is four hours. Each unit
of x1 has an incremental profit of Rs.12/= and each unit of x2 an incremental profit of
Rs.4/=.
(a) Formulate the Primal problem.
(b) Write the dual problem to the above primal problem.
(c) Solve the dual problem and by using it find the solution for the primal problem.

The above part (a) is I done as follows; Mathematical formulation is

To maximize : $Z=12a+4b$ --> Equation 01

Subject to constraints :

$3a+2b \le 6$ --> Equation 02

$\frac {1}{2} a+b \le 4$ --> Equation 03

$a \ge 0, b \ge 0$ --> Equation 04

If the above it true plz give me a help to find the other part (b) and (c) or help me to find the answer
• December 9th 2009, 10:06 PM
mrfloyd