a.	CoffeeTime is considering selling juices along with its other products. 
                	        	States of Nature
 	 	      High Sales	Med. Sales	Low Sales
 	 	      A(0.2)	        B(0.5)	        C(0.3)
A1 (sell juices)      3000	        2000	        -6000
A2 (don't sell juices)	0	         0	          0
					

The probabilities shown above represent the states of nature and the
decision maker's (e.g., manager) degree of uncertainties and personal
judgment on the occurrence of each state. What is the expected payoff
for actions A1 and A2 above? What would be your recommendation?
Interpret the results based on practical considerations.

If possible please answer by tomorrow.

Hi!!

Expected payoff for A1:
E(A1) = p(high sales)*3000 + p(Med sales)*2000 + p(low sales)*(-6000) = 
      = 0.2*3000 + 0.5*2000 + 0.3*(-6000) =
      = -200
The expected payoff for selling juices is -$200 .

Expected payoff for A2:
E(A2) = 0.2*0 + 0.5*0 + 0.3*0 = 0
The expected payoff for not selling juices is $0 (we did not need
calculations for this conclusion, did us?).

According the above calculations, based on theoritecal assumtions the
better recommendation is to not sell juices.
But based on practical considerations it could be a good idea to take
the risk and sell juices. Note that the probability of making high or
medium sales is 0.2+0.5 = 0.7 which is more than twice the probability
of making low sales (0.3). So in the real world there will be some
high or medium sales, and according with the probabilities, they might
offset the low sales giving some earning.
This lead us to the assumtion that the decision will be taken
according to how risk averse (or not) is the manager. But they usually
get paid based on sales commisions, regardless if they are low or
high, so in this scenario he will feel inclined to take the risk; even
if he is paid in profit-sharing basis, he will take the risk anyway
with the intention of increase the annual bonus. In a situation like
this he has more to gain than to lose.


I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards,
livioflores-ga

Thank you for your excellent answer and fast response time. I really
appreciate the time you took to help out.