Question

This assignment involves solving a decision tree problem and summarizing the results.

please type out response, do not write them. be sure to clearly show your decision tree and all supporting calculations.

Acme Inc. is considering marketing one of two new video games: Galaxy Wars or Quasar Trek. Galaxy Wars is a distinctive game and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand are as follows:

Galaxy Wars	High	Medium	Low
Profit	900	850	250
Probability	0.20	0.55	0.25

Quasar Trek is a less distinctive game and is assumed that it may experience some market competition. Estimated profits (in thousands of dollars) with and without competition is as follows:

With Competition (Quasar Trek)	High	Medium	Low
Profit	750	300	150
Probability	0.25	0.45	0.30
Without Competition (Quasar Trek)	High	Medium	Low
Profit	1600	800	400
Probability	0.60	0.30	0.10

a. Develop a decision tree for the Acme Inc. problem.

b. Acme Inc. believes there is a 0.55 probability that its competitor will produce a new game similar to Quasar Trek. Given this probability of competition, the director of planning recommends marketing the Galaxy Wars video game. Using the expected monetary value as the basis for your decision, what is your recommended decision?

c. Use sensitivity analysis to determine what the probability of competition for Quasar Trek would have to be for you to change your recommended decision alternative.

d. Based on your decision tree, what is the Expected Value of Sample Information (EVSI)? Briefly summarize the meaning of this value.

Answer 1

(a) Decision tree is a sequential tool that is represented in the form of a graph.It helps in process of decision making over a period of time.

(b) RECOMMENDED DECISION USING EXPECTED VALUE

Expected value for GALAXY WARS

It is given the probabilities $900, $850 , $250

Let us calculate the Expected value for GALAXY WARS with competition

EV(Galaxy wars) = 0.2(900)+0.55(850) +0.25(250)

= 180 + 467.5 + 62.5 = 710

Expected value for QUASAR TREK with competition

EV(Quasar trek with competition) =0.25(750) + 0.45(300) + 0.30(150)

= 187.5 + 135 + 45 = 367.5

Expected value for QUASAR TREK without competition

EV(Quasar trek without competition) = 0.60(1600) + 0.30(800) + 0.10(400)

= 960 + 240 + 40 = 1240

It is given that probability of Quasar trek with competition is 0.55 and without competition is 0.45.

Let us calculate the Expected value of Quasar trek

EV(Quasar trek)= 0.55(367.5) + 0.45(1240)

= 202.125 + 558 = 760.125

Hence QUASAR TREK should be recommecnded with the Expected value of $760.125 which is better than the Expected Value of GALAXY WARS.

(c) Graphical Sensitivity Analysis to determine probability of competition for QUASAR TREK.

Let P be the probability of Competition

Now calculate the value of P by solving the equation of Expected value of Quasar trek with competition and without competition.

1240 - P(1240-367.5) = 710

1240 - 710 = 872.5P

P= 0.6074

The value of P is higher than 0.74 before making a change in Galaxy wars game.