- 1 Marks
Question
A company makes two products X and Y. It takes 2¼ hours to make one unit of X and 3¾ hours to make one unit of Y. If only 18,000 direct labour hours are available, then the production time constraint is expressed as
A. 3.75x + 2.25y ≤ 18,000
B. 2.25x + 3.75y ≤ 18,000
C. 3.75x + 2.25y ≥ 18,000
D. 2.75x + 3.75y ≥ 18,000
E. 3.75x + 2.25y = 18,000
Answer
Answer: B
Explanation:
The correct answer is B (2.25x + 3.75y ≤ 18,000). Here’s how we arrive at this solution:
- For product X: 2¼ hours = 2.25 hours
- For product Y: 3¾ hours = 3.75 hours
- Let x be the number of units of product X and y be the number of units of product Y.
- The total time used for production cannot exceed the available time: (Time for X * Number of X) + (Time for Y * Number of Y) ≤ Total available time 2.25x + 3.75y ≤ 18,000
- This is a “less than or equal to” constraint because the company cannot use more than the available 18,000 hours, but it can use less.
Therefore, the correct expression of the production time constraint is 2.25x + 3.75y ≤ 18,000.
- Tags: Linear Programming, Production Constraints, Time Management
- Level: Level 1
- Topic: Operations Research
- Series: MAY 2016
- Uploader: Kwame Aikins