A political scientist has reserved birr 3200 a grant to fund a research project. Undergraduate students, graduate students and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct 18 interviews and be paid birr 100. Each graduate student will conduct 25 interviews and be paid birr 150. Each faculty member will conduct 30 interviews and be paid birr 200. Due to transportation facilities, no more than 20 interviewers can be hired. Required:Formulate appropriate LPM for the above problem to determine the number of undergraduate, graduate and faculty members that must be hired to maximize profit?How many undergraduate students, graduate students and faculty members must be hired to maximize profit?What is the maximum number of interviews?

Question

A political scientist has reserved birr 3200 a grant to fund a research project. Undergraduate students, graduate students and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct 18 interviews and be paid birr 100. Each graduate student will conduct 25 interviews and be paid birr 150. Each faculty member will conduct 30 interviews and be paid birr 200. Due to transportation facilities, no more than 20 interviewers can be hired. Required:Formulate appropriate LPM for the above problem to determine the number of undergraduate, graduate and faculty members that must be hired to maximize profit?How many undergraduate students, graduate students and faculty members must be hired to maximize profit?What is the maximum number of interviews?

Answer 1

To solve this problem, we can use the concept of Linear Programming Model (LPM) to determine the number of undergraduate students, graduate students, and faculty members that need to be hired to maximize profit.

Let's define our decision variables:
Let x1 = Number of undergraduate students to be hired
Let x2 = Number of graduate students to be hired
Let x3 = Number of faculty members to be hired

Objective Function:
We want to maximize the profit made from the interviews conducted. The profit can be calculated by multiplying the number of interviews conducted by the payment for each interviewer.

Profit = (18 * 100 * x1) + (25 * 150 * x2) + (30 * 200 * x3)

Constraints:
1. Total number of interviewers cannot exceed 20:
x1 + x2 + x3 ≤ 20

2. The grant is limited to Birr 3200 (budget constraint):
(100 * 18 * x1) + (150 * 25 * x2) + (200 * 30 * x3) ≤ 3200

3. The number of interviews conducted by each type of interviewer:
x1 ≤ 18 (Undergraduate students can conduct a maximum of 18 interviews)
x2 ≤ 25 (Graduate students can conduct a maximum of 25 interviews)
x3 ≤ 30 (Faculty members can conduct a maximum of 30 interviews)

Now we can solve this LPM to determine the optimal number of undergraduate students, graduate students, and faculty members to be hired.

To solve this, you can use a mathematical optimization tool or software like Excel Solver, MATLAB, or any other optimization software. Set up the objective function, constraints, and solve for the values of x1, x2, and x3 that maximize the profit.

After solving the LPM, the values of x1, x2, and x3 will represent the number of undergraduate students, graduate students, and faculty members to be hired, respectively, in order to maximize profit.

To find the maximum number of interviews, you can calculate it using the values of x1, x2, and x3:
Maximum number of interviews = (18 * x1) + (25 * x2) + (30 * x3)

By plugging in the values obtained after solving the LPM, you can find the maximum number of interviews conducted.

Please note that the exact values of x1, x2, x3, and the maximum number of interviews can only be determined by solving the LPM using appropriate optimization software.