In this task, you are asked to formulate the linear programming problem below and then solve it.

A sub-contractor produces two types of units for a kitchen manufacturer, a base unit (B) and cabinet unit (C).

The base unit requires 40 minutes in the production department and 50 minutes in the assembly department.

The cabinet unit requires 30 minutes in the production department and 20 minutes in the assembly department.

The production and assembly of these two units are done by specialist carpenters who are in short supply. Each day only 14 hours in the production department are available and only 8 hours are available in the assembly department.

Once sold, the base units contribute 30 to profit and the cabinet units 40 to profit.

Required:

Formulate the Linear Programming problem above by defining the control variables, stating the object function and the constraints.

You are required to produce the graph for all inequalities and clearly show the feasible region. (Copy image to Word)

Find the quantity of units to maximise profit.