13–21
very close to maximizing the mean profit. The order quantity that actually maximizes
mean profit is probably somewhere between these two quantities.
Order Quantity (250)
Order Quantity (275)
Order Quantity (300)
Order Quantity (325)
Order Quantity (350)
$119.74 $125.08 $125.02 $118.83 $107.24
c)
13.16
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5
6
7
8
9
10
11
12
A B C D E
Purchase Price $100
Selling Price $150
Order Quantity 14
Value Probability
Demand 14 Discrete (Custom) 10 0.05
11 0.1
Revenue $2,100 12 0.1
Purchase Cost $1,400 13 0.15
Total Profit $700 14 0.2
15 0.15
16 0.1
13–23
$0 profit.
b) Thirteen tickets maximizes Susan’s mean profit.
13–24
c)
13–25
d) Thirteen tickets is the optimal order quantity found by OptQuest.
13.17
a) A bid of approximately $5.3 million maximmizes the mean profit.
OurBid (5.200)
OurBid (5.250)
OurBid (5.300)
OurBid (5.350)
OurBid (5.400)
OurBid (5.450)
OurBid (5.500)
OurBid (5.550)
OurBid (5.600)
0.473 0.486 0.489 0.488 0.480 0.463 0.392 0.311 0.241
13–26
b) The optimal bid is approximately $5.305 million, as found by Optquest.
13.18
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2
3
4
5
6
7
8
9
10
11
12
13
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19
20
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A B C D E
Data
Our Project Cost ($million) 5.000
Our Bid Cost ($million) 0.050
Competitor Bids Competitor 1 Competitor 2 Competitor 3 Competitor 4
Bid ($million) 6.083 6.083 6.083 6.083
Distribution Triangular Triangular Triangular Triangular
Competitor Distribution Parameters (Proportion of Our Project Cost)
Minimum 105% 105% 105% 105%
Most Likely 120% 120% 120% 120%
Maximum 140% 140% 140% 140%
Competitor Distribution Parameters ($millions)
Minimum 5.250 5.250 5.250 5.250
Most Likely 6.000 6.000 6.000 6.000
Maximum 7.000 7.000 7.000 7.000
Minimum Competitor
Bid ($million) 6.083
Our Bid ($million) 5.700
Win Bid? 1 (1=yes, 0=no)
Profit ($million) 0.650
13–28
approximately 51.6%.
b) A bid of approximately $5.5 million maximizes RPI’s mean profit.
Our Bid (5.300)
Our Bid (5.400)
Our Bid (5.500)
Our Bid (5.600)
Our Bid (5.700)
Our Bid (5.800)
Our Bid (5.900)
Our Bid (6.000)
0.248 0.324 0.361 0.354 0.311 0.222 0.141 0.060
13–29
c)
13–30
d) The optimal bid is approximately $5.55 million, as found by Optquest.
13.19 a) A long-term loan of approximately $5 million maximizes Everglades’s mean ending
balance.
LT Loan (0.00)
LT Loan (5.00)
LT Loan (10.00)
LT Loan (15.00)
LT Loan (20.00)
5.73 6.72 5.82 3.07 –0.33
13–31
b)
13–32
c) The optimal long-term loan is approximately $5.87 million, as found by Optquest.
13.20 Merrill Lynch launched the Management Science Group to deal with the issues raised by
the rise of electronic trading in the late 1990s. The group studied various product structure
and pricing alternatives. They focused on two main pricing options, viz., an asset-based
“The benefits were significant and fell into four areas: seizing the marketplace initiative,
13–33
13.21 a) Accepting approximately 185 reservations maximizes the mean profit.
ReservationsToAccept (180)
ReservationsToAccept (181)
ReservationsToAccept (182)
ReservationsToAccept (183)
ReservationsToAccept (184)
ReservationsToAccept (185)
ReservationsToAccept (186)
ReservationsToAccept (187)
ReservationsToAccept (188)
ReservationsToAccept (189)
ReservationsToAccept (190)
$6,613 $6,719 $6,803 $6,869 $6,908 $6,926 $6,924 $6,894 $6,841 $6,777 $6,693
b)
13–34
c) The optimal number of reservations to accept is approximately 185, as found by
OptQuest.
13.22
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A B C D E F
Airline Overbooking
Discount
Data Reservations
Seats Available 112
to Accept 75
Fixed Cost $10,000
Discount Fare $150
Total
Full Coach Fare $400
Reservations
Cost of Bumping $600
to Accept 120
Discount Ticket Demand (Triangular)
Minimum 50 Discount-Fare Demand 96.66666667
Most Likely 90 Rounded 97
Maximum 150 Tickets Purchased 75
Probability to Show Up 95% Number that Show 71.25
Full-Coach Ticket Demand (Uniform) Full Coach Demand 50
Minimum 30 Rounded 50
Maximum 70 Tickets Purchased 45
Probability to Show Up 85% Number that Show 38.25
Number Denied Boarding 0
Number of Filled Seats 109.5
Revenue (Discount Fare) $11,250
Revenue (Full Coach) $15,300
Bumping Cost $0
Fixed Cost $10,000
Profit $16,550.00
13–36
a)
13–37
b)
Discount to Accept (50)
Discount to Accept (60)
Discount to Accept (70)
Discount to Accept (80)
Discount to Accept (90)
Total to Accept (112) $14,234.40 $14,627.05 $14,202.90 $13,117.10 $11,818.25
Total to Accept (117) $14,467.20 $15,284.45 $15,263.50 $14,518.70 $13,348.45
Total to Accept (122) $14,503.80 $15,668.65 $15,909.10 $15,334.70 $14,161.65
Total to Accept (127) $14,503.80 $15,725.25 $15,948.30 $15,263.50 $13,920.25
Total to Accept (132) $14,503.80 $15,715.05 $15,789.50 $14,923.30 $13,423.25
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