A student has at most 6 hours a day to study Mathematics and Physics. She wants to spend at least 1 hour on Physics, and the time spent on Mathematics should be at least twice the time spent on Physics. If she studies Mathematics for x hours and Physics for y hours a day, then the constraints (besides \(x \ge 0\), \(y \ge 0\)) are
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(x + y \le 6\), \(y \ge 1\), \(x \ge 2y\)
Each condition is written as one linear inequality:
Total time at most 6 hours: \(x + y \le 6\)
Physics at least 1 hour: \(y \ge 1\)
Mathematics at least twice Physics: \(x \ge 2y\)
Why the other options are incorrect
Option (1) \(x + y \le 6\), \(y \ge 1\), \(y \ge 2x\) — Incorrect. \(y \ge 2x\) says Physics is at least twice Mathematics, the reverse of the condition.
Option (2) \(x + y \ge 6\), \(y \ge 1\), \(x \ge 2y\) — Incorrect. “At most 6 hours” needs \(\le\), not \(\ge\).
Option (3) \(x + y \le 6\), \(x \ge 1\), \(x \ge 2y\) — Incorrect. The 1-hour minimum is for Physics, which is y, not x.