Problem $1$

The World$-$Light Company produces two light fixtures $($products $1$ and $2)$ that require both metal

frame parts and electrical components. Management wants to determine how many units of each

product to produce so as to maximize profit. For each unit of product $1,1$ unit of frame parts and

$2$ units of electrical components are required. For each unit of product $2,3$ units of frame parts

and $2$ units of electrical components are required. The company has $200$ units of frame parts and

$300$ units of electrical components. Each unit of product $1$ gives a profit of $$1,$ and each unit of

product $2$ gives a profit of $$2.$

a$)$ Formulate the problem as an LP model.

b$)$ Use the graphical method to find the optimal solution.