Chapter 3, Problem 22RP

Explanation of Solution

Formulation of LP:

Let,

$x_1$ and $x_2$ be the number of product 1 and 2 produced on machine 1 in the month 1

$y_1$ and $y_2$ be the number of product 1 and 2 produced on machine 2 in the month 1

$x_3$ and $x_4$ be the number of product 1 and 2 produced on machine 1 in the month 2

$y_3$ and $y_4$ be the number of product 1 and 2 produced on machine 2 in the month 2

The tabular representation of above is shown below,

	Month 1		Month 2
	Machine 1	Machine 2	Machine 1	Machine 2
Product 1	$x_1$	$y_1$	$x_3$	$y_3$
Product 2	$x_2$	$y_2$	$x_4$	$y_4$

Then the LPP becomes,

Maximize, $\text{Revenue=55}\left({\text{x}}_{\text{1}}{\text{+y}}_{\text{1}}\right)\text{+12}\left({\text{x}}_{\text{3}}{\text{+y}}_{\text{3}}\right)\text{+65}\left({\text{x}}_{\text{2}}{\text{+ y}}_{\text{2}}\right)\text{+32}\left({\text{x}}_{\text{4}}{\text{+y}}_{\text{4}}\right)$