A social science professor has received a grant to fund a research project involving voting trends in the Philippines. The budget of the grant includes P32,000 for conducting a door-to-door interviews the day before the election. College students, graduate students and faculty members will be hired to conduct the interviews. Each college student will conduct 18 interviews and be paid P1,000. Each graduate student will conduct 30 interviews and be paid P1,500. Each faculty member will conduct 25 interviews and be paid P2,000. Due to limited transportation facilities, no more than 20 interviewers can be hired. How many undergraduate students, graduate students and faculty members should be hired in order to maximize the number of interviews that will be conducted. What is the maximum number of interviews? *(Let x be the number of college students to be hired, y the number of graduate students to be hired. z the number of faculty members to be hired and I the number of interviews) * (a) In the initial tableau, what is the entering variable? In the initial tableau, what is the leaving variable? (b) How many iteration(s) was/were made to obtain the optimal solution? (c) What is the optimal solution to the problem?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Problem:
A social science professor has received a grant to fund a research project involving voting trends in the Philippines. The budget of the grant includes P32,000 for conducting a door-to-door interviews the day before the election. College students, graduate students and faculty members will be hired to conduct the interviews. Each college student will conduct 18 interviews and be paid P1,000. Each graduate student will conduct 30 interviews and be paid P1,500. Each faculty member will conduct 25 interviews and be paid P2,000. Due to limited transportation facilities, no more than 20 interviewers can be hired. How many undergraduate students, graduate students and faculty members should be hired in order to maximize the number of interviews that will be conducted. What is the maximum number of interviews? *(Let x be the number of college students to be hired, y the number of graduate students to be hired. z the number of faculty members to be hired and I the number of interviews) *
(a) In the initial tableau, what is the entering variable? In the initial tableau, what is the leaving variable?
(b) How many iteration(s) was/were made to obtain the optimal solution?
(c) What is the optimal solution to the problem?
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