Chapter 6.6, Problem 2P

Explanation of Solution

Duals of LP:

• Consider the linear programming problem given below:
• max z= $50x_1+100x_2$
• Subject to constraints:
  • $7x_1+2x_2\ge 28$
  • $2x_1+12x_2\ge 24$
  • $x_1,x_2\ge 0$
• To find the dual of the above LP proceed as follows:

Max z
min z	($y_1\ge 0$)	($y_2\ge 0$)	Cost(in thousands of dollars)
	$y_1$	$y_2$
$\left(x_1\ge 0\right)$	$x_1$	7	2	$\le 50$
$\left(x_2\ge 0\right)$	$x_2$	2	12	$\le 100$
	$\ge 28$	$\ge 24$

• The dual is:
• min w=$28y_1+24y_2$