I need assistance in the following: This assignment must be in Excel/QM and subm
ID: 2934217 • Letter: I
Question
I need assistance in the following:
This assignment must be in Excel/QM and submitted through Assignment. Also provide a written response for each part of each question.
3.1) A manager needs to hire short-term employees to meet production demands. The manager would like to hire one of three possible short-term workers. Ten hours are demanded with 50% probability, 20 hours are demanded with 30% probability, and 30 hours are demanded with 20% probability. The table below represents the alternatives and possible states of nature.
States of Nature
(Worker hrs. demanded)
Alternatives
10 hr. total pay
20 hr. total pay
30 hr. total pay
Worker 1
$1,000.00
$1,800.00
$2,400.00
Worker 2
$900.00
$1,800.00
$2,500.00
Worker 3
$950.00
$1,750.00
$2,500.00
a) Which alternative will minimize the expected monetary value?
b) What is the expected value of perfect information?
3.2) The following payoff table provides profits based on various possible decision alternatives and various levels of demand.
States of Nature
Demand
Alternatives
Low
Medium
High
Alternative 1
80
120
140
Alternative 2
90
90
90
Alternative 3
50
70
150
The probability of a low demand is 0.4, while the probability of a medium and high demand is each 0.3.
(a) What decision would an optimist make?
(b) What decision would a pessimist make?
(c) What is the highest possible expected monetary value?
(d) Calculate the expected value of perfect information for this situation.
3.3) Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that any leftover goods will have to be scrapped. How many units should be ordered in February?
States of Nature
(Worker hrs. demanded)
Alternatives
10 hr. total pay
20 hr. total pay
30 hr. total pay
Worker 1
$1,000.00
$1,800.00
$2,400.00
Worker 2
$900.00
$1,800.00
$2,500.00
Worker 3
$950.00
$1,750.00
$2,500.00
Explanation / Answer
3.1) a.) We are given the probabilities for the different worker hours and hence, we just need to plug in the probabilities with the costs of the workers to find the the expected monetary value of each worker and hence, minimize it.
Worker 1 = 1000*0.5 + 1800*0.3 + 2400*0.2 = 500 + 540 + 480 = 1520
Worker 2 = 900*0.5 + 1800*0.3 + 2500*0.2 = 450 + 540 + 500 = 1490
Worker 3 = 950*0.5 + 1750*0.3 + 2500*0.2 = 475 + 525 + 500 = 1500
Hence, Worker 2 will generate lowest costs.
b.) EVPI (Expected value of Perfect Information) is the maximum amount one is willing to pay for additional information.
EXPI = EVwPI -- EVwoPI = Expected value WITH PI - Expected Value WITHOUT PI {PI -- Perfect Information}
EVwPI means the best possible values of each state from the given alternatives multiplied by their porbabilities which here would be = 900*0.5 + 1750*0.3 + 2400*0.2 = 450 + 525 + 480 = 1455
EVwPI = 1490 (Minimum of EV)
EVPI = 1490 - 1455 = 35
3.2) i) Optimist is one who would expect the demand to be high/medium and thus, expect profits for those states. Thus, he will choose Alternative 1 which has profits of 120 and 140 for medium and high respectively (each has probability of 0.3)
ii) A pessimist would not assume that the state would be good and hence, would be inclined towards a expected LOW state and hence, Alternative 2 gives him the best and stable profits. (90 through the states).
iii) EMV or EV = Maximum out of the expected values of each alternatives.
Alternative 1 = 80*0.4 + 120*0.3 + 140*0.3 = 32 + 36 + 42 = 110
Alternative 2 = 90*0.4 + 90*0.3 + 90*0.3 = 90
Alternative 3 = 50*0.4 + 70*0.3 + 150*0.3 = 20 + 21 + 45 = 86
Thus, Alternative 1 is the best with EMV = 110
iv) EVPI = EVwPI - EVwoPI
EVwoPI = EMV = EV = 110
EVwPI = Best profits in each state multiplied by their porbabilties = 90*0.4 + 120*0.3 + 150*0.3 = 36 + 36 + 45 = 117
Thus, EVPI = 117 - 110 = 7.
3.3) Expected Profit per unit = $30
Expected Demand = 0.4*50 + 0.5*60 + 0.1*70 = 20 + 30 + 7 = 57 units. [Answer]
Because left over will have to scrapped off, thus that will incur a loss of $20 per unit (cost price).
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