Social Science
Business
Operations and Supply Chain Management (14th Edition)
Exercise 8
Chapter 20, Page 544
Operations and Supply Chain Management
ISBN: 9789339204105
Table of contents
Solution
Verified
Answered 9 months ago
Step 1
1 of 11
In this task, we will calculate the expected profit in part a) and calculate how
many pies should be baked in order to maximize the expected profit.
Step 2
2 of 11
The following is given:
Price to make
Sell price
Salvage price
$6.75
$17.99
$0.99
We are also given a table that we will call the demand-probability table.
Step 3
3 of 11
a)
In this part, we will calculate the expected profit if the company bakes 15 apple
pies each day.
Step 4
4 of 11
Let's start by calculating the profit of selling a single pie.
Profit = Sell price − Price to make
​
= $17.99 − $6.75
​
= $11.24
Step 5
5 of 11
Now we will multiply the profit from one pie by 15 in order to get the expected
profit from selling 15 apple pies.
15 × $11.24 = $168.6
Therefore, we conclude that the expected profit from selling 15 pies is gonna be
$168.6.
Step 6
6 of 11
b)
We will start solving this task by calculating the cost of underestimating the
demand. If we underestimate the demand we lose the difference between the
selling price and the price to make.
Cu = Sell price − Price to make
​
​
= $17.99 − $6.75
= $11.24
​
Step 7
7 of 11
Now, the next step is calculating the cost of overestimating the demand. We can
find this cost by subtracting the salvage price from the price to make.
Co = Price to make − Salvage price
​
​
= $6.75 − $0.99
​
= $5.76
Step 8
8 of 11
Now let's calculate the probability of the product not being sold. For that, we
will use the following formula.
P ≤
Cu
Co + Cu
​
​
​
​
Step 9
9 of 11
Now by substituting the cost of overestimating and underestimating into the
mentioned formula we get the following:
P ≤
Cu
Co + Cu
​
​
≤
​
​
11.24
5.76 + 11.24
​
​
​
≤
11.24
17
​
≤ 0.661
From this, we conclude that the probability of the newspapers not being sold is
0.661.
Think about what should we do next?
Step 10
10 of 11
Now we will add another column to the demand-probability table and we will
call it cumulative probability.
Demand
Probability
Cumulative probability
5
10%
0.1
10
20%
0.1+0.2=0.3
15
25%
0.3+0.25=0.55
20
25%
0.55+0.25=0.8
25
15%
0.8+0.15=0.95
30
5%
0.95+0.05=1
Step 11
11 of 11
Now looking at the new table we see that our result P matches the demand for
20 apple pies.
Therefore, we conclude that in order to maximize expected profit company
should bake 20 apple pies.
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