The national government procured a total of 1550 test kits for the five regions in the country. If the distribution will be solely based on the total number of PUIS and PUMS combined in the region. How many test kits will each region receive? Assume that the total population of the five regions is 560,506. Regions A B CDE E PUIs and PUMs Population (by percent) 10% 15% 20% 30% 25%
The national government procured a total of 1550 test kits for the five regions in the country. If the distribution will be solely based on the total number of PUIS and PUMS combined in the region. How many test kits will each region receive? Assume that the total population of the five regions is 560,506. Regions A B CDE E PUIs and PUMs Population (by percent) 10% 15% 20% 30% 25%
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve this in Hamilton's Method.
Transcribed Image Text:The national government procured a total of 1550 test kits for the five
regions in the country. If the distribution will be solely based on the
total number of PUIs and PUMS combined in the region. How many
test kits will each region receive? Assume that the total population of
the five regions is 560,506.
Regions
A
B
CDE
PUIs and PUMS Population (by
percent)
10%
15%
20%
30%
25%
Transcribed Image Text:HAMILTON'S METHOD
Problem Set:
Region
A
B
C
D
E
Total
Population
56,056
84,076
112,101
168,152
140,127
560,506
PUI and PUI SQ
(in
percentage) Quota)
10%
15%
20%
30%
25%
100%
●
Sample Problem (As a guide to answer prob set)
STEPS
1. Determine how many people each representative should
represent.
o
o
Do this by dividing the total population of all
stated by the total number of representatives
Answer is called the standard divisor or
divisor
2. Divide each state's population by the divisor to
determine how many representative it should have
O Record answer to several decimal places
O Answer is called the quota
Since we can only allocate whole (number) representatives,
Hamilton resolves the whole number problem, as follows:
3. Cut of all the decimal parts of all the quotas (but don't
forget what the decimals were)
(Standard
O These are called the lower quotas
o Sum will always be less than or equal to the total
number of representatives
4. Assuming the total from Step 3 was less than the total
number of representatives, assign the remaining
representatives, one each, to the states whose decimal
Cs Scoparts of the quota were the largest, until the desired total
is reached.
The summation for SQL is either exactly the total number
of objects or less than
O It can never be greater than the desired number to
apportion
DECISION: The number of representative of Stated A, B, C, and
D are 4, 6, 8, and 12 respectively.
Quota Rule
o Says that the final number of representative a state
gets should be within one of the state's quota.
Since, we're dealing with whole numbers for our final
answers, that means that each state should either go
up to the next whole number above its quota, or
down the next whole number below its quota
SQL
(Standard
Quota
Lower)
SAMPLE PROBLEM
Consider a country with 4 states and 30 seats in Congress and
populations distributed as in the table below
States
A
B
C
D
Total
Step 1. Compute the Standard Divisor
SD =
=
States
A
B
C
D
Total
States
A
B
Step 2. Compute the Standard Quota or Quota per state (SQ)
Population per State
SQ =
SD
Population
27500
38300
с
D
Total
No. of Test
kits by
Hamilton's
Plan
Total Population
Number of People to Apportion
: 6300
189000
30
46500
76700
189000
Step 3. Use the concept of Lower Quota (SQL)
o Whole number of the Standard Quota
States
SQ
Population
27500
A
4.3651
B
38300
6.0794
46500
Population
27500
38300
46500
76700
189000
Population
27500
38300
46500
76700
189000
SQ
4.3651
6.0794
7.3809
12.1746
7.3809
12.1746
с
D
76700
Total
189000
Step 4. If the total of the SQL is not the same with the total number
of population, choose the SQ with the highest decimal and add 1
to its corresponding SQL;. Do this until the total of the SQL is the
same with the total population.
SQ
4.3651
6.0794
7.3809
12.1746
4
6
7
12
29
SQL
4
6
7
12
Number of
SQL Representatives by
Hamilton Plan
4
6
8
12
30
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