A small construction company has 3 employees A, B, and C and it manufactures wooden doors and windows. It makes a profit of ` 600 and ` 450 respectively for every door and window that it sells. Employee A makes 4 doors a day while employee B makes 6 windows per day. The employee C is a painter and can paint 18 m2 per day. Each wooden door requires a paint of 4 m2 and wooden window requires a paint of 2 m2. How many doors and windows should the company produce each day to maximize total profit?

a. Formulate the linear programming model for this problem.

b. Use graphical method to solve this model.

c. In order to face the competition from another wooden door manufacturer, if the company decides to lower his profit from ` 600 per wooden door to ` 400 per wooden door, how would the optimum solution change (if it changes at all).

d. What will happen to the optimal solution of the original data if the employee ‘A’ decides to lower his working hours and instead of 4 doors, makes only 3 doors a day?