Week 2 Assignment - Linear Programming
docx
keyboard_arrow_up
School
American Public University *
*We aren’t endorsed by this school
Course
312
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
4
Uploaded by courtneyhanley2
Week 2 Assignment: Linear Programming
Courtney Hanley
BUSN312: Operations Research
Dr. Shelley Pumphrey
January 14, 2024
Problem 1 Answer:
Objective:
Maximize Z = 300R1+ 400R2
Constraints:
Input Crude A: 5R1 + 4R2 ≤
200
Input Crude B: 3R1 + 5R2 ≤
150
Output Gasoline X: 5R1 + 4R2 ≥
100
Output Gasoline Y: 8R1 + 4R2 ≥
80
Non-Negative Constraints: R1, R2 ≥
0
Solution:
Z=300 (30) + 400 (12) =Rs. 13800. The manager should undertake 30 runs from process 1, and 12 runs from process 2. The max profit is Rs. 13800.
Problem 2 Answer:
Objective: Minimize Z = X1 + X2 + X3 + X4 + X5 + X 6
Constraints: Requirements for each time period: X1+ X6 ≥ 20 (period 1) X2+ X1 ≥ 50 (period 2) X3+ X2 ≥ 80 (period 3) X4+ X3 ≥ 100 (period 4) X5+ X4 ≥ 40 (period 5) X6+ X5 ≥ 30 (period 6)
Each policeman works eight consecutive hours: X1+ X2+ X6 ≥ 8 (period 1)
X2+ X3+ X1 ≥ 8 (period 2) X3+ X4+ X2 ≥ 8 (period 3) X4+ X5+ X3 ≥ 8 (period 4) X5+ X6+ X4 ≥ 8 (period 5) X6+ X1+ X5 ≥ 8 (period 6)
Non-Negative Constraints: X1, X2, X3, X4, X5, X6 ≥ 0
Solution:
X1 = 20, X2 = 30, X3 = 50, X4 = 70, X5 = 40, X6 = 30 The police department should schedule 20 policemen to start work in period 1, 30 in period 2, 50
in period 3, 70 in period 4, 40 in period 5, and 30 in period 6.
Problem 3 Answer:
Objective: Maximize Z = 80,000X1 + 175,000X2 + 75,000X3 + 250,000X4
Constraints:
The car dealer wants to invest Rs. 20,00,000 in his deals. The total cost of purchasing cars should
not exceed Rs. 20,00,000. 60,000X1 + 150,000X2 + 55,000X3 + 220,000X4 ≤ 2000000
The car dealer wants to maintain the rates of purchase of cars as 3: 1: 2: 4. X1 + 3X2 + 2X3 + 4X4 ≤ 2000000
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Non-Negative Constraints: X1, X2, X3, X4 ≥ 0
Solution:
X1 = 600,000, X2 = 200,000, X3 = 400,000, X4 = 1,000,000. The car dealer should buy 600,000 units of car A, 200,000 units of car B, 400,000 units of car F, and 1,000,000 units of car G.
Problem 4 Answer: