3. Suppose that Mr Smith is co-owner of Smith and Associates Tyres. He is currently considering expanding his business empire of manufacturing tires. Suppose that Mr Smith is an optimistic decision maker. On the contrary, Mr Khumalo who co-owns Smith and Associates Tyres is a pessimistic decision maker. Assume that their options of getting new machinery is as summarized:

Machinery	Favourable Market	Unfavourable Market
Option 1	R3 000 000	- R 2 000 000
Option 2	R 2 200 000	- R 900 000
Option 3	R 800 000	- R 100 000
Option 4	R 4 000 000	- R 3000 000

3.1.1 What type of decision making is faced in this scenario?

3.1.2 Separately, what decision criterion should Smith and Khumalo adopt given that they are optimistic and pessimistic, respectively?

3.1.3 Expanding on the table above, show with calculations and explanations, what is the best alternative (either Option 1, 2, 3 or 4) for Smith and Khumalo, separately?

3.1.4 Suppose that a well-respected industry expert estimates that the probabilities of favourable and unfavourable markets are equal to 0.8 and 0.2, respectively. A concerned Mr Smith wants to use these probabilities to determine the optimal decision:

- What decision model should be used and why?

- Determine the optimal decision using the decision model chosen above.

3.2. An investment firm is considering opening an arcade in a neighbourhood with a lot of schools. If the arcade demand is favourable, the firm could realize a net profit of R250 000. If the arcade demand is unfavourable, they could lose R120 000. Note that if they decide not to construct the arcade, there is a cost of zero Rands. Assuming that there is an equal chance that the arcade will be successful / fail:

- Construct a decision tree to help visualize this scenario.

- Should the firm proceed to construct the arcade?