I need help with this question: A country library system has 4 branches. Seven n

Question

I need help with this question: A country library system has 4 branches. Seven new librarians are to be assigned according to the number of books at each library. The books are distributed accordingly.

a) What is the standard divisor? Show all work.

b) Fill in the standard quota, upper quota, and lower quota for each branch in the chart above. Show your work.

C ) Use Hamilton’s method to assign the appropriate assignment in the chart above. Show your work.

Branch A B C Total Books 1,556 1,328 365 3,249 Standard Quota Lower Quota Upper Quota Assignment

Explanation / Answer

a) Standard divisor = Total number of books/ total number of librarians

                         = 3249/7 = 464.1429

b) Standard quota = Number of books in the branch/ Standard divisor

Therefore, for A, Std. quota = 1556/464.1429 =3.3524

   For B = 1328/464.1429 = 2.8611

For C =365 / 464.1429= .7864

Lower quota is obtained by rounding down the standard quota

Upper quota is obtained by rounding up the standard quota

Hamiltonian method of assigning libarians

1. find the standard divisor . Here it is 464.1429

2. assigned lower quota to each branch. in case of C, since its lower quota is 0, it is assigned1.

3. So now, the total assignment is 3+2+1 = 6. One more librarian is there to assign.

4. Now check the lower quota of branches with largest fractional part. that is B(2.8611). the remaining librarian has been assigned to B. Now the total assignment = 3+3+1 =7

Branch A B C Total Books 1556 1328 365 3249 Standard quota 3.3524 2.8611 .7864 6.9999 Lower quota 3 2 0 Upper Quota 3 3 1 7 Assignment 3 3 1 7

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