Question

A Saskatchewan farm machinery manufacturing company has developed a prototype of two machinery models (A and B). The manufacturer wishes to select one of these machines for further manufacturing. Also the manufacturer is under no obligation to select any of these 2 machines. The company has hired you to make a recommendation to the manufacturer not eh selection of the best alternative. In further discussion with the manufacturer you select the following attributes of the decision problem: a) manufacturers major motivation in selecting the best farm machinery in economic-improve the level of earnings for the company b)major uncertainty facing the selection process is future markets. Given above attributes, you decide to undertake a market survey, which resulted in 3 possible types of markets: Bouyant, steady state and Depressed. You also estimated the there are 3 types of markets prevail 50:20:30 percent, respectively, of the time in the future. You also estimated the net revenues of the company from sales of 2 types of machinery in thousands of dollars shown below:

Pariculars	Bouyant	Steady State	Depressed Market
A	2200	800	1000
B	3500	1500	-1000
Neither	0	0	0

Using a decision three model, provide your recommendation to the farm machinery manufacturing company.

Answer 1

The company has 3 options to choose from

1. Buy Model A
   1. If the market is Bouyant (with a probability, P(Bouyant)=0.50) then make a revenue of $2,200 (in thousands), if the market is steady state (with a probability, P(steady state) = 0.20), then make a revenue of $800 (thousands) if the market is Depressed (with a probability, P(Depressed) = 0.30), then make a revenue of $1,000 (thousands).
2. Buy Model A
   1. If the market is Bouyant (P(Bouyant)=0.50) then make a revenue of $3,500 (in thousands), if the market is steady state (P(steady state) = 0.20), then make a revenue of $1,500 (thousands) if the market is Depressed (P(Depressed) = 0.30), then make a revenue of -$1,000 (thousands).
3. Do not buy either
   1. The revenue then is zero irrespective of the market.

The decision tree is below

moving from the right to left.

Chance node 2: Manufacture model A. The expected value of this node is

Chance node 3: Manufacture model B. The expected value of this node is

Decision node 1:

The company has to choose from 3 options

1. Option 1: Manufacture machine model A, with an expected net revenue=$1,560 (thousands)
2. Option 2: Manufacture machine model B, with an expected net revenue=$1,750 (thousands)
3. Option 3: Manufacture Neither , with a net revenue=$0

Option 2 provides the highest expected revenue of these 3 choices. Hence the company should go for manufacturing machine B