Consider wider problems：练习题

A delivery company uses two identical vans to deliver 160 packages per day. One van is taken out of service for repairs. The manager decides to increase the working hours of the remaining van by \( 25\% \) to help cover the loss. Assuming the delivery rate per hour remains constant, what is the new total number of packages that can be delivered daily?

An irrigation reservoir holds 50,000 litres of water. Every day, 2% of the current volume is lost to evaporation. A farmer draws a fixed 1,500 litres daily. A new covering system is proposed that would reduce evaporation to 0.5% daily but requires a cleaning process that uses 200 litres of water daily. What is the difference in the reservoir volume after exactly 2 days between the original and the new system (starting from a full 50,000 litres)?

A call center requires 20 operators to be on the phones at all times during a 12-hour day. Currently, operators work 4-hour shifts with no breaks. The center considers switching to 6-hour shifts, but labor laws then require a 30-minute unpaid break in the middle of each shift. During this break, another operator must cover the phone. If an operator is paid only for time spent on the phones, how many more total operator-hours must the company pay for in a 12-hour day to ensure 20 people are always on the phones compared to the original system?

A driver currently completes a 300 km journey in 5 hours, including a single 30-minute rest stop. Due to new safety regulations, the driver must now take a 20-minute break for every 100 km traveled. Assuming the driving speed remains the same, how much longer will the journey take under the new regulations compared to the old ones?

A circular shuttle bus route has a total loop time of 40 minutes. 4 buses are used to maintain a consistent 10-minute frequency between shuttles. The city decides to extend the route to include a new shopping district, which increases the total loop time by 12 minutes. If the city wants to maintain the original 10-minute frequency, how many additional buses must be added to the fleet, and what would the frequency be if no buses were added?

A medical clinic uses a scheduling model that predicts total patient time based solely on an average consultation length of \(15\) minutes per person. However, data shows patients consistently spend \(40\%\) more time in the clinic than predicted.

Suggest two distinct real-world factors that should be incorporated into the model to improve its predictive accuracy.

A factory operates a 'Just-in-Time' model, receiving \(500\) units of a component every Monday morning. A new regional transport tax increases the cost of each delivery by \(\$200\), regardless of the quantity delivered.

Identify the impact on the current weekly delivery model and explain how the model parameters (frequency and batch size) should be adjusted to minimise the impact of this fixed cost increase.

A delivery company uses a pricing model where the cost \(C\) is \(C = 5 + 1.5d\), where \(d\) is the distance in kilometres. Due to a fuel price increase, the company decides to increase the per-kilometre rate by 20% but keep the fixed fee the same. What is the new cost for a 10 km delivery?<\/p>

A community center holds a weekly yoga class. Currently, the class runs from 18:00 to 19:30 every Tuesday, and the attendance is consistently 20 people. The center is considering moving the class to 17:30 to 19:00 to allow a second class to start at 19:15.

Identify two potential impacts this change in timing might have on the current attendees' ability to attend the class, and suggest one way the center could mitigate a negative impact.