QUESTION ONE A company is facing heavy demand for one of its products; the existing manufacturing facility is working at full capacity on normal shift. The firm has two options to meet heavy demand i. Either institute over time an option that will cost the firm Sh 2 million or ii. Install new machinery, at a cost of sh 200 million The choice between the two options depends mainly on what happens to sales over the next two years. During the first year, the firm estimates that there is 70% chance for sales increase and a 30% chance of fall in sales. If a new machine had been installed at the beginning (time zero) and sales had risen, then management would either install a second machine or institute overtime. If these two happened, then the sales forecast will be either high (20% chance) or medium (70% chance) or low (10% chance). In the event that the second machine is installed, the anticipated payoffs are as follows: Sh 80 M, 60 M and 50 M respectively for high, medium and low sales. However, if overtime is constituted, the payoffs are estimated at Sh 60 M, 50 M and 40 M respectively for high, medium and low sales. If a new machine had been installed and sales had fallen, the decision maker would have no choice but to use the existing capacities to the fullest. The anticipated payoffs for this are estimated at Sh 50M, 40 M and 20 M respectively for high, medium and low sales. If over time, had been instituted initially and sales had risen, management would have two options open: either install a new machine with anticipated payoffs of Sh 60 M, 50 M and 20 M respectively for high, medium and low sales or install a new machine and use overtime with similar payoffs. If overtime had been instituted initially and sales had fallen, management would have only one option available, that is, institute over time with anticipated payoffs of Sh 40 M, 40 M and 20 M respectively for high, medium and low sales Required: i. Draw and properly label the decision tree ( 8 Marks) ii. Evaluate the tree and determine the optimal strategy ( 2 Marks) QUESTION TWO A market gardener is planning his production for next season, and he has asked you as a