BDS4614 / BDS2074 – MANAGEMENT DECISION SCIENCE
INSTRUCTIONS TO STUDENT
1. This Assignment is a Group Assignment of not more than 2 students and consists of 5 pages with 5 Questions only.
2. Answer all the questions. All questions carry equal marks and the distribution of the marks for each question is given.
3. The hard copy of the answer booklet must be printed and must be submitted to your respective lecturer/ tutor on or before 18 January 2013 QUESTION 1
A political scientist has received a grant to fund a research project involving voting trends. The budget of the grant includes $3200 for conducting door-to-door interviews the day before an election. Undergraduate students, graduate students, and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct 18 interviews and be paid $100. Each graduate student will conduct 25 interviews and be paid $150. Each faculty member will conduct 30 interviews and be paid $200. Due to limited transportation facilities, no more than 20 interviewers can be hired. The scientist’s objective is to determine how many undergraduate students, graduate students and faculty members should be hired in order to maximize the number of interviews.
a. Formulate the given problem as a linear programming problem. [4 marks]
The problem is solved using a software and the following output is obtained.
Objective Function Value = 520.000
|Variable |Value |Reduced Cost | |X1 |0.000 | 2.000 | |X2 |16.000 | 0.000 | |X3 | 4.000 | 0.000 |
|Constraint |Slack/Surplus |Dual Price | |1 |0.000 |10.000 | |2 |0.000 |0.1 |
OBJECTIVE COEFFICIENT RANGES
|Variable |Lower Limit |Current Value |Upper Limit | |X1 |No Lower Limit |18.000 |20.000 | |X2 |24 |25.000 |30.000 | |X3 |25 |30.000 |32.000 |
RIGHT HAND SIDE RANGES
|Constraint |Lower Limit |Current Value |Upper Limit | |1 |16.000 |20.000 |21.3333 | |2 |3000.000 |3200.000 |4000.000 |
b. Give the complete optimal solution.
c. What are the dual prices for the two constraints?
What interpretation does this have?
Over what range can the objective function coefficient of X3
vary before a new solution point becomes optimal?
By how much can the amount of resource 2 decrease before the dual price will change?
What would happen if the first constraint's right-hand side increased by 7 and the second's decreased by 150? [4 marks]
[Total 20 marks]
The Maju Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year and the super market is open throughout the year. Each box costs $4 and it costs the store $60 per order of Munchies, and it costs $0.80 per box per year to keep the cereal in stock. Once an order for Munchies is placed, it takes 4 days to receive the order from a food distributor.
Find the optimal order quantity.
b. Find the total...
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