A company manufactures $2$ types of products X and Y$.$ The raw material required to

manufacture the products is limited to $1$ kg per week. Product X requires half a kg and

Y requires half a kg of the raw material in order to make the products. X requires $2$

units of labour and Y requires $2$ units of labour. At least $8$ units of labour is available

in a week. Product X gives a profit of Rs $3/$unit where Product Y gives a loss of Rs

$2/$unit$.$ However, the company wants to have a product mix in a said week. Formulate

the problem as a linear programming problem and solve using graphical