# Finicky's Jeweler's

## The Problem

Finicky's Jewelers sells watches for \$50 each. During the next month, they estimate that they will sell 15, 25, 35, or 45 watches with respective probabilities of 0.35, 0.25, 0.20, and ... (figure it out). They can only buy watches in lots of ten from their dealer. 10, 20, 30, 40, and 50 watches cost \$40, 39, 37, 36, and 34 per watch respectively. Every month, Finicky's has a clearance sale and will get rid of any unsold watches for \$24 (watches are only in style for a month and so they have to buy the latest model each month). Any customer that comes in during the month to buy a watch, but is unable to, costs Finicky's \$6 in lost goodwill.

Find the best action under each of the four decision criteria.

## The Solution

### Creating the Payoff Table

Demand 15
qty desc unit ext
10 bought -40 -400
10 sold 50 500
5 goodwill -6 -30
total   70
qty desc unit ext
20 bought -39 -780
15 sold 50 750
5 clearance 24 120
total   90
qty desc unit ext
30 bought -37 -1110
15 sold 50 750
15 clearance 24 360
total   0
qty desc unit ext
40 bought -36 -1440
15 sold 50 750
25 clearance 24 600
total   -90
qty desc unit ext
50 bought -34 -1700
15 sold 50 750
35 clearance 24 840
total   -110
Demand 25
qty desc unit ext
10 bought -40 -400
10 sold 50 500
15 goodwill -6 -90
total   10
qty desc unit ext
20 bought -39 -780
20 sold 50 1000
5 goodwill -6 -30
total   190
qty desc unit ext
30 bought -37 -1110
25 sold 50 1250
5 clearance 24 120
total   260
qty desc unit ext
40 bought -36 -1440
25 sold 50 1250
15 clearance 24 360
total   170
qty desc unit ext
50 bought -34 -1700
25 sold 50 1250
25 clearance 24 600
total   150
Demand 35
qty desc unit ext
10 bought -40 -400
10 sold 50 500
25 goodwill -6 -150
total   -50
qty desc unit ext
20 bought -39 -780
20 sold 50 1000
15 goodwill -6 -90
total   130
qty desc unit ext
30 bought -37 -1110
30 sold 50 1500
5 goodwill -6 -30
total   360
qty desc unit ext
40 bought -36 -1440
35 sold 50 1750
5 clearance 24 120
total   430
qty desc unit ext
50 bought -34 -1700
35 sold 50 1750
15 clearance 24 360
total   410
Demand 45
qty desc unit ext
10 bought -40 -400
10 sold 50 500
35 goodwill -6 -210
total   -110
qty desc unit ext
20 bought -39 -780
20 sold 50 1000
25 goodwill -6 -150
total   70
qty desc unit ext
30 bought -37 -1110
30 sold 50 1500
15 goodwill -6 -90
total   300
qty desc unit ext
40 bought -36 -1440
40 sold 50 2000
5 goodwill -6 -30
total   530
qty desc unit ext
50 bought -34 -1700
45 sold 50 2250
5 clearance 24 120
total   670

### Payoff Table

Buy 10 Buy 20 Buy 30 Buy 40 Buy 50 70 90 0 -90 -110 10 190 260 170 150 -50 130 360 430 410 -110 70 300 530 670

### Opportunistic Loss Table

Buy 10 Buy 20 Buy 30 Buy 40 Buy 50 20 0 90 180 200 250 70 0 90 110 480 300 70 0 20 780 600 370 140 0