Question $2$

$(10$ points$)$ You are an operations manager at XYZ Manufacturing, a company that produces two

types of decorative items: Type A and Type B$.$ Each type of item must undergo two key stages in

its production process: assembly and finishing. The time required for each stage of production for

both types of items is as follows:

Each unit of Type A requires $1$ hour of assembly and $2$ hours of finishing.

Each unit of Type B requires $2$ hours of assembly and $1$ hour of finishing.

Due to operational constraints, the total available hours for assembly and finishing each week are

limited to $100$ hours for each process. The profit generated from the sale of each unit of Type A is

$$30,$ and for Type B$,$ it's $$40.$

Formulate a linear programming model to determine how many units of each product type XYZ

Manufacturing should produce each week to maximize its total profit. Define your decision variables,

write down the objective function, and specify all the constraints.