Answer the following Essay Type Questions (6 ×3=18) SportXpert company manufactu
ID: 3173932 • Letter: A
Question
Answer the following Essay Type Questions (6×3=18)
SportXpert company manufactures sport bikes. It assesses its fixed costs at 81,000 SAR for a year. Each mountain bike carries on average a variable cost of 300 SAR. SportXpert sells every bike at a price of 1,200 SAR.
Determine the number of bikes that the company must sell to reach its break-even point.
Assuming that the company manufactures 180 sport bikes per year (regular activity over the year). What will be its benefit?
Consider the following payoff (profit) table
State of nature
Action
Which action would an optimistic (maximax) decision maker choose?
Which action would a pessimistic (maximin) decision maker choose?
Consider the same payoff (profit) table given in question 2. Assume also that the probabilities of the three states of natures are given as follows.
State of nature
What is the best alternative using the expected monetary value analysis?
Compute the Expected Value of Perfect Information
Consider the statement given in question 3. What is the best alternative using the expected opportunity loss analysis?
Bike sales at SportXpert are shown below:
Week
Bike Sales
1
4
2
5
3
4
4
6
5
5
6
7
7
-
Develop a 3-week weighted moving average forecast by weighting the three weeks as follows:
Weights Applied
Period
4
Last week
3
Two weeks ago
1
Three weeks ago
8
Total
SportXpert want to use the simple exponential smoothing on the bike sales given in question 5. Assume that F1 is perfect.
Develop a simple exponential smoothing with a=0.3 and compute the MAD.
The MAD of a simple exponential smoothing with a=0.4 is 0.87. What value of a (0.3 or 0.4) should SportXpert choose?
State of nature
Action
1 2 3 a 10 20 50 b 5 30 40Explanation / Answer
Solution
Back-up Theory
Let n = Number of bikes sold per year,
F = fixed cost,
V = Variable cost per unit,
S = Selling Price per unit
Then, Total cost, C = F + n.V …….. (1)
Sales revenue, R = n.S ……………..(2)
Profit, P = R – C = n(S - V) – F ……(3)[assuming that all that is produced is also sold]
For break-even n, we should have
R = C or R – C = 0 or
n(S - V) – F = 0 ………………..….. (4)
Or, break-even n = F/(S - V) ……… (5)
For the Decision /Theory questions, optimistic strategy (maximax) is that strategy which gives max of row maxes and pessimistic strategy (maximin) is that strategy which gives max of row mins …………………………………………………………….(6)
Now, to work out the solution,
Given F = 81000, V = 300 and S = 1200
Part (a)
Given F = 81000, V = 300 and S = 1200
Break-even n = 81000/(1200 - 300) [vide (5) under Back-up Theory ]
= 90 ANSWER
Part (b)
Given F = 81000, V = 300, per production = 180, and S = 1200
Benefit per year = (180 x 1200) – {81000 – (180 x 300)}
= 81000 ANSWER
Part (c)
The pay-off table and required computations are given below:
Action
State of Nature
Row max
Row
1
2
3
min
a
10
20
50
50
10
b
5
30
40
40
5
For optimistic strategy, max of row max is for action ‘a’ ANSWER
Part (d)
With reference to the table under Part (c),
Max of row min happens for action ‘a’. Hence, pessimistic strategy is action ‘a’ ANSWER
Action
State of Nature
Row max
Row
1
2
3
min
a
10
20
50
50
10
b
5
30
40
40
5