A firm makes x units of product A and y units of product B a day. Each unit of A needs 2 hours on machine M1 and 1 hour on machine M2, and each unit of B needs 1 hour on M1 and 3 hours on M2. Machine M1 is available for 14 hours and M2 for 17 hours a day. Both machines are used for their full available time when the daily production (x, y) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \((5, 4)\)
Both machines are fully used when both constraints hold with equality:
\(2x + y = 14\) (machine M1)
\(x + 3y = 17\) (machine M2)
From the first, \(y = 14 - 2x\). Then
\(x + 42 - 6x = 17\)
\(x = 5\)
\(y = 14 - 10 = 4\)
This point (5, 4) is the corner point where the two constraint lines meet.
Why the other options are incorrect
Option (2) \((4, 5)\) — Incorrect. M1 time is \(8 + 5 = 13\) hours, not 14.
Option (3) \((6, 2)\) — Incorrect. M2 time is \(6 + 6 = 12\) hours, not 17.
Option (4) \((3, 8)\) — Incorrect. M2 would need \(3 + 24 = 27\) hours, more than 17.