Question 1C Technology Inc needs to decide how many of the new Ipads to purchase
ID: 448195 • Letter: Q
Question
Question 1C
Technology Inc needs to decide how many of the new Ipads to purchase for the new store. The company has assumed that demand will be 60, 110,180 or 220 Ipads next month and they need to decide whether to order 60,110,180 or 220 Ipads for this period. Each Ipad cost Technology Inc 2500 and can be sold for $4,000. Technology Inc can sell any unsold Black berry back to their supplier for $$500.00.
Number if IPads demanded
Amount ordered
60
110
180
220
60
90,000
110
-10,000.00
180
270,000
220
-55,000
Complete the payoff table
Using a optimistic approach (maxima), which option would you choose?
Using a pessimistic approach, which option would you choose?
If you are a La Place decision maker, what option would you choose?
If you are Hurwicz decision maker, which option would you choose in =0.75
Using a minimax regret approach, which option would you choose?
Using the same Probabilities of 0.20, 0.35, 0.25 and 0.20, for possible level of demand respectively, which decision alternative will maximise the expected profit?
What is the most the firm should be willing to pay to obtain further (perfect) information (EVPI)?
Use the alternative method to verify EVPI
Number if IPads demanded
Amount ordered
60
110
180
220
60
90,000
110
-10,000.00
180
270,000
220
-55,000
Explanation / Answer
Profit if Ipad is sold =4000-2500=1500
Loss in case ipad is not sold=500-2500=-2000
Payoff =Number of ipad sold*1500-Number of ipad unsold*2000
Thus if Amount ordered is 110 and quantity demanded is 180 then only 110 can be sold and profit=110*1500=165000
if Amount ordered is 110 and quantity demanded is 60 then only 60 can be sold and remaining 50 will be unsold
Thus payoff =60*1500-50*2000=-$10000
Number if IPads demanded
Amount ordered
60
110
180
220
60
90,000
90,000
90,000
90,000
110
-10,000
1,65,000
1,65,000
1,65,000
180
-1,50,000
25,000
2,70,000
2,70,000
220
-2,30,000
-55,000
2,10,000
3,30,000
1)
Optimistic or Maxima: One with maximum payoff will be choosen. Maximum payoff in the table is $330,000. Thus Amount ordered will be 220
2)
Minima or Pessimistic: One with minimum loss will be chosen or Max of minimum will be choosen
Minimum is when amount ordered is 60 unit and maximum payoff when amount ordered is 60 unit is against 60 unit ordered. Thus amount ordered will be 60 unit
3)
La Place decision maker will assume all the vent has equal probability and thus probability of demand 60,100,180,220=0.25 each
Thus expected payoff when amount ordered is 60 unit=(90000+90000+90000+90000)/4=90000
Expected payoff when amount ordered is 110 unit=(-10000+165000+165000+165000)/4=121250
Expected payoff when amount ordered is 180 unit=(-150000+25000+270000+270000)/4=103750
Expected payoff when amount ordered is 220 unit=(=-230000-55000+210000+333000)/4=63750
Thus maximum expected payoff is when quantity ordered is 110 unit
4)
Hurwicz decision maker will give weight 0.75 to optimistic payoff and 0.25 to pessimistic pay0ff for each amount ordered
Hurwicz payoff when amount ordered is 60 unit=90000*0.25+90000*0.75=90000
Hurwicz payoff when amount ordered is 110 unit=-10000*0.25+165000*0.75=121250
Hurwicz payoff when amount ordered is 180 unit=-150000*0.25+270000*0.75=165000
Hurwicz payoff when amount ordered is 220 unit=-230000*0.25+333000*0.75=192250
Thus Maximum Hurwicz payoff is when quantity ordered is 220 unit
Number if IPads demanded
Amount ordered
60
110
180
220
60
90,000
90,000
90,000
90,000
110
-10,000
1,65,000
1,65,000
1,65,000
180
-1,50,000
25,000
2,70,000
2,70,000
220
-2,30,000
-55,000
2,10,000
3,30,000
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