1Write each statement as a mathematical sentence: (a) Suresh takes at most 2 hours to reach school from home. (b) A Nepali citizen must be at least 16 years old to get citizenship. (c) Rupesh has Rs. 750 to buy pens at Rs. 15 each and copies at Rs. 25 each.
2Can the three inequalities \( x \le 2 \), \( x \ge 16 \) and \( 15x + 25y \le 750 \) be shown on a graph? Describe each graph.
3Show on graphs: (a) \( x \ge 0 \) (b) \( x \le 0 \) (c) \( y \ge 0 \) (d) \( y \le 0 \).
4Show on graphs: (a) \( x > -1 \) (b) \( x < 2 \).
5Show the inequality \( 2x + 3y \le 6 \) on a graph.
6Show \( 3x + 4y \le 12 \), \( 2x - y \le 2 \), \( x \ge 0 \) and \( y \ge 0 \) on one graph. If the inequalities enclose a common region, what is it called? Shade it and state your conclusion.
7A shaded region is bounded by line AB through \( A(-1, 0) \) and \( B(0, 2) \), and line CD through \( C(0, 3) \) and \( D(4, 0) \). Both lines are solid and the origin is in the shaded region. Find the inequalities the region represents.
8Show \( x + y > 4 \) on a graph.
9Show \( y \ge 2x \) on a graph. Why can the origin not be used as the test point here?
10Why is the boundary of \( x + 2y < 8 \) drawn dotted but the boundary of \( x + 2y \le 8 \) drawn solid?
11Does the point \( (2, 1) \) lie in the solution region of \( 2x + 3y \le 6 \)? Does \( (1, 1) \)?
12Find the vertices of the feasible region of \( x + y \le 5 \), \( x \ge 0 \) and \( y \ge 0 \), and show that each vertex satisfies all three inequalities.