A family plans to buy adult tickets and child tickets for entry to a botanical garden
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A family plans to buy adult tickets and child tickets for entry to a botanical garden. Let x denote the number of adult tickets and y denote the number of child tickets. The following conditions apply:
• Each adult ticket costs Rs 30 and each child ticket costs Rs 15.
• The family can spend at most Rs 150 on tickets.
• At least one adult ticket must be bought.
• The garden management does not allow negative tickets.
Answer the questions below.
(a) Formulate a system of linear inequalities in x and y representing all the above conditions.
(b) Draw the graph of every inequality obtained in part (a), decide for each boundary whether it is solid or dashed, and state the direction of shading after testing a suitable point.
(c) Shade the feasible region representing all possible ticket combinations.
(d) Verify whether the point (2,4) lies inside the feasible region, showing calculations for every inequality.