The Amarant Furniture Company wants to use mathematical programming to

determine the optimal number of two of its couch models: Gerdoo and Baloot.

Market research indicates that at most $48$ of the Gerdoo model and $12$ of the

Baloot model can be sold per month. The maximum number of work$-$hours

available is $720$ per month. A Gerdoo couch requires $18$ work$-$hours, and a

Baloot couch requires $12$ work$-$hours. Each Gerdoo couch sold produces a profit

of $150,$ and each Baloot couch produces a profit of $100.$

a$)$

Formulate a linear programming model for this problem.

b$)$

Use the graphical method to solve this model.

$1$