Choosing a Workshop Plan
Your family is planning to attend 'Science Sunday' at a community center in Yamagata. The notice gives two sessions. Morning: 'Robot Programming,' 9:30-11:30, ¥500 per person, for ages 10 and up; children under 10 must be with an adult. Afternoon: 'Paper Bridge Challenge,' 13:00-15:00, ¥300 per person, for ages 8 and up; children under 8 must be with an adult. Your group is you (15), your sister (11), your brother (7), and your mother. Your mother can attend only in the afternoon. Your brother wants to join at least one session. The family budget for fees is ¥1,500, and lunch is not included. The morning session has only three seats left; the afternoon has many seats. Your sister says, 'I want to do the robot session, but I don't want to go alone.'
1. Which session(s) can your brother attend, and who must be with him? Explain using the age and adult rules.
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Your brother is 7. The morning Robot Programming session is for ages 10 and up, and children under 10 must be with an adult. Your mother is not available in the morning, and you (15) and your sister (11) are not adults, so the brother cannot attend the morning session. The afternoon Paper Bridge Challenge is for ages 8 and up, but children under 8 must be with an adult. Your mother can attend in the afternoon, so the brother can join the afternoon session with her. That meets his 'at least one session' wish. The answer depends on matching each age rule to the adult who is actually free at that time.
2. A classmate proposes: you and your sister do the morning robot session; your mother and brother do the afternoon session. Test this proposal against seats, cost, and your sister's condition. What is the binding constraint?
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Morning: you and your sister are 15 and 11, both 10+, so no adult is needed. The session has three seats left, so two seats are available. Your sister does not want to go alone, and you are with her, so her condition is met. Cost: 2 × ¥500 = ¥1,000. Afternoon: mother ¥300 + brother ¥300 = ¥600. Total = ¥1,600. The budget is ¥1,500, so the proposal fails by ¥100. Seats and age rules are satisfied; the binding constraint is the fee budget. A correct answer must do all three checks, because a plan can pass the age and seat rules and still fail on money.