Question
In: Economics
Sierra Mountain Bike, Inc., is a producer and wholesaler of rugged bicycles designed for mountain touring....
Sierra Mountain Bike, Inc., is a producer and
wholesaler of rugged bicycles designed for mountain touring. The
company is considering an upgrade to its current line by making
high-grade chrome alloy frames standard. Of course, the market
response to this upgrade in product quality depends on the
competitor’s reaction, if any. The company’s comptroller projects
the following annual profits (payoffs) following resolution of the
upgrade decision:
States of Nature
Sierra’s No
Decision Competitor
Competitor
Alternatives Upgrade Upgrade
Upgrade $1,000,000 $1,500,000
Do not upgrade 800,000 2,000,000
Determine the decision alternative that Sierra would
choose given a maximin criterion? Explain your choice of answer
.
Calculate the opportunity loss or regret matrix for the Competitor
Upgrade.
Calculate the opportunity loss or regret matrix for the No
Competitor Upgrade.
Which decision alternative would Sierra choose given a minimax
regret criterion?
Solutions
Expert Solution
| States of nature |
No Competitor Upgrade S1 |
Competitor Upgrade S2 |
|---|---|---|
| Alternatives | ||
| A1 | 1000000 | 1500000 |
| A2 | 800000 | 2000000 |
# Maximin Criterion-----
* The course of action that maximizes the minimum possible pay- off is selected .
At first , minimum value of each row is selected
Out of these maximum value out of selected row minima is the decision criterion.
| States of nature | S1 | S2 | Row Minima |
|---|---|---|---|
| Alternatives | |||
| A1 | 1000000 | 1500000 | 1000000 |
| A2 | 800000 | 2000000 | 800000 |
Out of row minima, column maxima ( maximum vale out of minima) is 800000, which belongs to A2.
So, As per Maximin criterion, decision alternative is do not upgrade
# Opportunity loss / Regret Matrix--------
* The regret table is formulated below by substracting all the elements of each column fro highest value for that column
* After that, using Minimax Regret Criterion, Minimum of these maximum regrets , corresponding to decision alternative should be selected.
| States of nature | S1 | S2 | Maximum Regret |
|---|---|---|---|
| Alternatives | |||
| A1 |
0 (1000000--1000000) |
500000 (2000000--1500000) |
500000 |
| A2 |
200000 (1000000--800000) |
0 (2000000--2000000) |
200000 |
Minimum of maximum regret is 200000 in A2.
so, Decision criterion under Minimax Regret is not to upgrade.
Rahul Sunny answered 2 years agoRelated Solutions
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The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a...
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Total
Dirt
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Sales
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Variable manufacturing and selling expenses
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Contribution margin
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20,500
Depreciation of special equipment
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15,500
Salaries of product-line managers
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The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a...
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Total
Dirt
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Mountain Bikes
Racing
Bikes
Sales
$
919,000
$
262,000
$
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$
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471,000
118,000
198,000
155,000
Contribution margin
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203,000
101,000
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69,300
8,300
40,700
20,300
Depreciation of special equipment
44,100
20,900
7,900
15,300
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The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a...
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expenses for the past quarter follow:
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Racing
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The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a...
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expenses for the past quarter follow:
Total
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Mountain Bikes
Racing
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Sales
$
918,000
$
261,000
$
404,000
$
253,000
Variable manufacturing and
selling expenses
462,000
114,000
196,000
152,000
Contribution margin
456,000
147,000
208,000
101,000
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69,500
8,600
40,800
20,100
Depreciation of special
equipment
44,000
20,200
7,800
16,000
Salaries of product-line
managers
116,100...
The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a...
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Total
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Racing
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$
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116,000
209,000
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145,000
200,000
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70,400
8,600
41,000
20,800
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44,400
20,900
7,600
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Total
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Racing
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$
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$
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selling expenses
477,000
117,000
209,000
151,000
Contribution margin
447,000
148,000
197,000
102,000
Fixed expenses:
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69,600
8,400
41,000
20,200
Depreciation of special
equipment
43,000
20,400
7,400
15,200
Salaries of product-line
managers
113,600...
The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a...
The Regal Cycle Company manufactures three types of bicycles—a
dirt bike, a mountain bike, and a racing bike. Data on sales and
expenses for the past quarter follow:
Total
Dirt
Bikes
Mountain Bikes
Racing
Bikes
Sales
$
924,000
$
267,000
$
404,000
$
253,000
Variable manufacturing and selling expenses
466,000
111,000
201,000
154,000
Contribution margin
458,000
156,000
203,000
99,000
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70,100
8,700
40,700
20,700
Depreciation of special equipment
43,500
20,200
7,900
15,400
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