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Math 115 – Homework Project #3
Name:
1. Ben likes chocolate three times as much as vanilla, and he likes vanillatwice as much
strawberry. Ben buys a Neapolitan cake (1/3 each of chocolate, vanilla and strawberry) for
$13.50.
(a) How much does Ben value each section of the cake?
(8)
(b) Ben is offered a piece of this cake that is made up of 20 chocolate, 15 vanilla, and 25
strawberry. How much is this piece worth to Ben? (4)
(c) If five people are going to share this cake, how much is a “fair share” to Ben?
(4)
2. Four people are going to divide a cake using the lone-divider method. The table below shows
how each person values each piece. Describe all possible fair divisions of the cake. (12)
Divider
Chooser 1
Chooser 2
Chooser 3
s1
25%
33%
35%
15%
s2
25%
20%
30%
28%
s3
25%
37%
25%
20%
s4
25%
10%
10%
37%
3. A cake is to be divided among 6 players (P1, P2, P3, P4, P5, P6) using the last diminisher method.
The players play in the order listed above. In round 1, P1 cuts a piece, and P2, P5, and P6 are
diminishers. In round 2 there are no diminishers. In round 3, after the first cut, each successive
player is a diminisher. (12)
(a) Which player gets his fair share at the end of round 1?
(b) Which player starts round 2?
(c) Which player is the last to have a chance to play or pass in round 2?
(d) Which player gets a fair share at the end of round 2?
(e) Which player starts round 3?
(f) Which player gets his fair share at the end of round 3?
4. Four players wish to divide up 5 items using the method of sealed bids. The bids are shown
below. Describe the outcome – including the division of any surplus money. (15)
A
$14000
$24000
$16000
$16000
$18000
Item 1
Item 2
Item 3
Item 4
Item 5
B
$12000
$15000
$18000
$16000
$24000
C
$22000
$33000
$14000
$18000
$20000
D
$17000
$34000
$15000
$16000
$21000
5. Three players agree to divide 12 items using the method of markers. The markers are shown
below. Describe the outcome. Which items are unclaimed? (10)
1
2
3
B1
4
5
A1 C1
6
7
C2
8
B2
9
10
11
12
A2
6. There are to be 250 faculty positions at a new university that are to be apportioned to 5
different schools based on enrollment projections. The enrollment projection for each school is
shown below.
School:
Enrollment:
(A) Agriculture (B) Business (E)Education (H)Humanities
1646
762
2081
1066
(a) What is the standard divisor for this apportionment situation?
(b) Complete the table below.
School
A
B
E
H
S
Total:
Std. Quota
(5)
(10)
Lower Quota
Upper Quota
(c) Use Hamilton’s method to apportion the faculty at this university.
(10)
(S)Science
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