Directions for questions: Refer to the following information regarding data…
2024
Directions for questions: Refer to the following information regarding data interpretation questions and answer them accordingly :
A factory employs three machines M1, M2 and M3 to manufacture three products X, Y and Z. Each machine runs for 12 hours a day. The following table gives the time taken (in minutes) by each machine to manufacture 1 unit of each of the products.
What is the maximum number of products that the three machines can manufacture in a day, if each machine manufactures only one type of product throughout the day?
- A.
345
- B.
123
- C.
212
- D.
543
Show answer & explanation
Correct answer: C
Concept: When each machine can be assigned to manufacture just one product for the whole day, the number of units it can produce equals its available time divided by the time it takes per unit. Since units produced is inversely related to time per unit, a machine maximizes its own output by making whichever product takes it the least time — and the day's maximum total is the sum of each machine's best individual output.
Each machine runs for 12 hours = 720 minutes a day.
For M1, the times are X = 12, Y = 18, Z = 10 minutes; the minimum is Z at 10 minutes, so M1 makes 720/10 = 72 units.
For M2, the times are X = 15, Y = 9, Z = 18 minutes; the minimum is Y at 9 minutes, so M2 makes 720/9 = 80 units.
For M3, the times are X = 16, Y = 15, Z = 12 minutes; the minimum is Z at 12 minutes, so M3 makes 720/12 = 60 units.
Total maximum units = 72 + 80 + 60 = 212.
Cross-check: since units produced = 720 / (time per unit), any other product choice on a machine has a larger time per unit and therefore yields fewer units than its row-minimum choice — so 212 is indeed the maximum achievable total.