3. Bole cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Birr 5 and that from a shade is Birr 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit? (Solve by simplex model).

A. Transform the above model into a standard form;

B. Write the initial tableau of the above model;

C. Determine the entering and leaving variables: and

D. Write the dual form of the model in

E. Compute the optimal solution