A company is about install a machine used in the manufacture of commercial appliances. Three suppliers have submitted tenders to supply the machine. The first supplier offers the A-Star machine, which makes parts of a recognised quality. The output from the machine is variable and could be up to 200 units per week (with probability of 0.3), between 201 and 300 per week (with probability of 0.55) or between 301 and 400 per week. All three outputs provide a notional profit for this machine of £4 per unit. The second supplier offers a B-Star machine, which produces an output of a higher quality. The output from this machine is also variable and can be up to 180 units per week (with probability 0.45) or between 181 and 200 units per week. Both outputs provide a notional profit for this machine of £12 per unit. The third supplier offers the C-Star machine, which can be set to produce either up to 240 high-quality units per week at a notional profit of £8 per unit, or between 241 and up to 270 medium-quality units per week at a notional profit of £7 per unit.

Required:

i. Produce a decision tree for this situation and obtain the optimal decision and the expected return using the expected monetary value technique. 

If production is 300 or more units per week, it is possible to sell all production as a single bulk order. Then there is a 70% chance of selling at 60% more profit, and a 30% chance of selling at 40% less profit.

ii. Produce a decision tree for this situation and obtain the optimal decision and the expected return using the expected monetary value technique. (hint: construct a second, similar tree but with the adjusted profit values).

Provide explanations and reasons to support the construction of your model and ensure you highlight any assumptions you make.

Also within your reflection section and, as additional information to the requested information contained in the rubric on page one above, you should address the strong and weak points in your model identified by sensitivity analysis. In particular, consider the manipulation of the data such that you can identify 'points of indecision' i.e. at a decision node when the payoffs in the various branches are identical whatever the choice of decision. Remember, that you are undertaking a time constrained assessment. 

All calculations should be clearly shown including all appropriate workings.