Sparkling Ltd is contemplating the manufacture of pool equipment and must decide whether to build a large or a small plant.

There is a 0.6 probability that the demand for the equipment will be strong and a 0.4 probability that the demand will be weak. If demand is strong and a large plant is built, a profit of R10 million will result. However if demand is weak but the plant is large, profits will amount to R1 million. If Sparkling Ltd builds a small plant and demand is weak, profits of R4million will be made.

If demand is strong and Sparkling Ltd has a small plant, the likelihood of competition is greater. It is estimated that there is a 75% chance that the company will come up against competition under these circumstances. In such a case, Sparkling Ltd could either build another separate small plant in a different area, or expand the existing plant. If Sparkling Ltd decides not to invest in further plant, profits of R6 million are expected, regardless of whether there is any competition.

 

If there is competition, however, either form of expansion is expected to yield a 0.7 probability of a profit of R8 million and a 0.3 probability of a profit of no change in the status quo. If there is no competition, building the separate plant would yield a profit of R9 million with a 0.8 probability and a profit of R7 million with a 0.2 probability.

Expanding the existing plant is expected to result in a profit of R7.5 million.

 

Required:

a. Draw a decision tree for Sparkling Ltd. 

b. Determine the optimal strategy by means of backward induction.