Answer:
Check Explanation
Step-by-step explanation:
Sale price = GHS80 per unit from first week of December to first week of January.
And at a reduced price of 30% from second week of January to the last week of January.
So, sales price for the second period = 70% × 80 = GHS56
To now find the profits for each of the purchase alternatives, we need to calculate the expected total demand
Expected demand units = (Demand × Probability)
First Period
Demand Probability | Expected demand units
500 0.1 | 50
600 0.3 | 180
750 0.4 | 300
850 0.2 | 170
Second period
Demand Probability | Expected demand units
320 0.5 | 160
180 0.3 | 54
130 0.2 | 26
Total expected demand units for first period = 50 + 180 + 300 + 170 = 700
Total expected demand units for second period = 160 + 54 + 26 = 240
i) When a pack of 600 products only is ordered, it is evident that it will cater for only the first period.
Expected Profit = (Expected sales it can cater for) - (Price of one pack of 600 products)
Expected sales it can cater for = 600 × 80 = GHS 48,000
Expected price of one pack of 600 products = 600 × 60 = GHS 36,000
Expected profit = 48000 - 36000 = GHS 12,000
ii) When a pack of 800 products only is ordered, it is evident that it will cater for the entire first period (700) and 100 from the second period.
Expected Profit = (Expected sales it can cater for) - (Price of one pack of 800 products)
Expected sales it can cater for = (700 × 80) + (100 × 56) = 56,000 + 5,600 = GHS 61,600
Expected price of one pack of 800 products = 800 × 57 = GHS 45,600
Expected profit = 61600 - 45600 = GHS 16,000
iii) When a pack of 1000 products only is ordered, it is evident that it will cater for the entire period, 700 and 240.
Expected Profit = (Expected sales it can cater for) - (Price of one pack of 1000 products)
Expected sales it can cater for = (700 × 80) + (240 × 56) = 56,000 + 13,440 = GHS 69,440
Expected price of one pack of 100 products = 1000 × 52 = GHS 52,000
Expected profit = 69440 - 52000 = GHS 17,440
iv) To do this, we first assume that
- the probabilities provided are very correct.
- the products are sold on a first come first serve basis
- the profits per unit for each period is calculated too.
Profit per product in this case = (16000/800) = GHS 20
For the first period
Expected profit = (700 × 80) - (700 × 57) = GHS 16,100
Average profit per unit = (16100/700) = GHS 23
For the second period
Expected profit = (100 × 56) - (100 × 57) = - GHS 100
Average profit per unit = (-100/100) = -GHS 1
Standard deviation = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = [700 × (23-20)²] + [100 × (-1-20)²]
= 6300 + 44,100 = 50,400
N = 800
Standard deviation per unit = √(50400/800) = GHS 7.94
Variance per unit = (standard deviation per unit)² = (7.94)² = 63.
Variance on 800 units = 800 (1² × 63) = 800 × 63 = 50,400
Standard deviation on profits of 800 units = √(50400) = GHS 224.5
v) With the same assumptions as in (iv), but now, we include the Profit (or more appropriately, the loss from unsold units of products)
Profit per product in this case = (17440/1000) = GHS 17.44
For the first period
Expected profit = (700 × 80) - (700 × 52) = GHS 19,600
Average profit per unit = (19600/700) = GHS 28
For the second period
Expected profit = (240 × 56) - (240 × 52) = - GHS 960
Average profit per unit = (960/240) = GHS 4
The expected unsold products = 1000 - 940 = 60
Profit on those unsold products = 0 - (60 × 52) = -GHS 3,120
Profit per unit = (-3120/60) = - GHS 52
Standard deviation = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = [700 × (28-17.44)²] + [240 × (4-17.44)²] + [60 × (-52-17.44)²]
= 78,059.52 + 43,352.064 + 289,314.816 = 410,726.4
N = 1000
Standard deviation per unit = √(410,726.4/1000) = GHS 20.27
Variance per unit = (standard deviation per unit)² = (20.27)² = 410.7264
Variance on 1000 units = 1000 (1² × 410.7264) = 800 × 410.7264 = 410,726.4
Standard deviation on profits of 1000 units = √(410,726.4) = GHS 640.88
vi) The standard deviation on profits show how much the real profits can range below or abobe the expected profit. That is, the standard deviation basically represents how big the risks or rewards can get.
A larger standard deviation will indicate a higher risk in case of loss and a higher reward in case of profits.
The option with the lower risk is the option with the lower standard deviation.
Hence, a pack of 800 products should be ordered instead of a pack of 1000 products as it has a lower standard deviation and hence, a lower risk attached to it thereby minimizing the risk.
Hope this Helps!!!