Answer To: BOSTON UNIVERSITY METROPOLITAN COLLEGE DEPARTMENT OF ADMINISTRATIVE SCIENCES AD 616: Enterprise Risk...
Swapnil answered on Apr 20 2021
79964/Solution.docx
1)
Recommended decision using expected value:
It is given that the probabilities are 0.2, 0.5, and 0.3, and the profits are $1,000, $700, and $300.
Now, calculate the expected value for space pirates with competition as follows:
EV (Battle Specific) = 0.2(1000) + 05(700) +0.3(300)
= 200 +350 + 90
= 640
Expected value for space pirates with competition:
It is given that the probabilities are 0.3, 0.4, and 0.3, and the profits are $800, $400, and $200.
Now, calculate the expected value for space pirates with competition as follows:
EV (Space pirates with competition) = 0.3(800) + 0.4(400) + 0.3(200)
=240 + 160 + 60
=460
Expected value for space pirates without competition:
It is given that the probabilities are 0.5, 0.3, and 0.2, and the profits are $1,600, $800, and $400.
Now, calculate the expected value for space pirates without competition as follows:
EV (Space pirates without competition) = 0.5(1600) + 0.3(800) + 0.2(400)
= 800 + 240 + 80
= 1120
Expected value for space pirates:
It is given that the probability of space pirates with competition is 0.6, and without competition is 0.4. The calculated expected value for space pirates with competition is 460, and without competition is 1,120.
Now, calculate the expected value for space pirates as follows:
EV (Space Pirates) = 0.6(460) + 0.4(1120)
= 276 + 448
=724
Hence, space pirates should be recommended with the expected value of $724,000, which is better than the expected value of battle pacific.
2)
Risk profile for space pirates:
The risk profile for the optimal decision is space pirates.
Now, construct a risk profile for the optimal decision as follows:
Profits (in thousands of dollars)
Probabilities
1,600
0.20(0.4 * 0.5)
800
0.30 [(0.6 * 0.3) + (0.4 * 0.3)]
400
0.32 [(0.6 * 0.4) + (0.4 * 0.2)]
200
0.18 (0.6 * 0.3)
Graphical sensitivity analysis for determining the probability of competition for space pirates:
Let p be the probability of competition.
Now, calculate the value of p by solving the equation for the expected value of space pirates with the competition and without the competition as follows:
1,120 – p (1,120 – 460) = 640
1,1,20 – 660p = 640
660p = 1,120 – 640
P = 0.73
The value of p is higher than 0.74 before making a change in the battle pacific game.
3)
A) A decision tree is basically gives the graphical representation of the decision problem that can give the sequential nature for the decision making process.
The expected value for the decision is the sum of weighted payoffs for the decision. The expected value (EV) of decision alternative di is defined as follows:
N
It gives us the number of nature states.
P(Sj)
It gives us the probability of the Sj nature
Vij
The payoff for the decision di and the state of Sj nature.
Calculating the expected value of d1
EV(d1) = (0.35) (-20) + (0.35) (40) +(0.30) (100)
= -7 + 14 + 30
= 37
Calculating the expected value of d2
EV(d2) = (0.35) (10) + (0.35) (45) +(0.30) (70)
= 3.5 + 15.75 + 21
= 40.25
Used the expected value approach, the recommended decision is d2 and we can expect...