City Guilds Model Questions Vol1 2020 Engineering Question 40

A workshop has three machines \(M_{1}, M_{2}, M_{3}\) that require preventive maintenance within a 24‑hour period. Each maintenance session lasts a whole number of hours and must satisfy the following constraints: 1. \(M_{1}\) needs at least 3 hours but no more than 5 hours. 2. \(M_{2}\) must be scheduled for a duration exactly twice that of \(M_{1}\). 3. \(M_{3}\) receives the remaining hours of the 24‑hour period after \(M_{1}\) and \(M_{2}\) are scheduled, and must be allocated at least 4 hours. 4. The hourly maintenance costs are ₦150 for \(M_{1}\), ₦200 for \(M_{2}\), and ₦180 for \(M_{3}\). The goal is to minimise the total maintenance cost while meeting all constraints. Determine the number of hours allocated to each machine and the minimum total cost in naira. Present your answer as a tuple "(h1, h2, h3, cost)".