Question

A factory wants to improve its service capacity by purchasing a new machine. Three different machines are available. The table below displays the estimated profits for all combinations of decisions with outcomes.

Decisions	States of Nature (Outcomes)
	High demand	Average demand	Low demand
Purchasing Machine A	$10000	$3000	$-4000
Purchasing Machine B	$6000	$4000	$-2000
Purchasing Machine C	$2000	$500	$0
Probabilities	0.5	0.2	0.3

Questions:

1. In case of uncertainty, apply the Maximax and Maximin criteria to find the corresponding best decision.
2. Use the expected monetary value (EMV) method to find the best decision.
3. A data analytic company proposed to the decision maker certain information about the market condition for $3000. Should the decision maker purchase the information for that price? Explain why.

and please the answer is typed

Answer 1

Maximum payoff for Purchasing Machine A Decision is 10000
Maximum payoff for Purchasing Machine B Decision is 6000
Maximum payoff for Purchasing Machine C Decision is 2000

According to Maximax criterion selected payoff is 10000 (As this is the maximum of the maximum payoffs) which belongs to Purchasing Machine A Decision

Minimum payoff for Purchasing Machine A Decision is -4000
Minimum payoff for Purchasing Machine B Decision is -2000
Minimum payoff for Purchasing Machine C Decision is 0

According to Maximin criterion selected payoff is 0 (As this is the maximum of the minimum payoffs) which belongs to Purchasing Machine C Decision

Expected monetary value (EMV) of Purchasing Machine A = 10000*0.5+3000*0.2+(-4000)*0.3 = 4400
Expected monetary value (EMV) of Purchasing Machine B = 6000*0.5+4000*0.2+(-2000)*0.3 = 3200
Expected monetary value (EMV) of Purchasing Machine C = 2000*0.5+500*0.2+0*0.3 = 1100

According to expected monetary value (EMV) method, best decision is Purchasing Machine A as this decision has highest EMV

Expected value of perfect information(EVPI) = expected monetary value with perfect information - expected monetary value without perfect information

=10000*0.5+4000*0.2+0*0.3-4400 = 1400

the decision maker should not purchase the information for that price as the Expected value of perfect information(EVPI) is only $1400 so there is no point in giving $3000 for information on market condition