Understand information in a variety of forms：練習問題

A logistics company manages three hubs (A, B, C) with specified capacities. Parcels flow between them daily. At the start of Day 1, all hubs are empty. The daily operations are:

• Each hub first processes its outgoing parcels.
• Then, it receives its initial daily incoming parcels.
• If, after receiving incoming parcels, the hub's total exceeds its capacity, the excess parcels are immediately diverted.
• Diversions occur in alphabetical order (A $$ \to $$ B $$ \to $$ C $$ \to $$ A $). Diverted parcels are added to the incoming count of the next hub for the same day's processing.

The daily parcel details are:

What is the final number of parcels stored at Hub A at the end of Day 1?

A clinic has three doctors (Dr. Singh, Dr. Lee, Dr. Chen) available for appointments between 9:00 AM and 1:00 PM. Each appointment slot is 30 minutes.

• Dr. Singh is available from 9:00 AM to 12:00 PM.
• Dr. Lee is available from 9:30 AM to 1:00 PM.
• Dr. Chen is available from 10:00 AM to 12:30 PM.

How many distinct 30-minute appointment slots are available across all doctors where at least two doctors are simultaneously available?

A research team is scheduling interviews with 6 participants (P1-P6) over two days. Each interview takes 1 hour. There are two interviewers (I1, I2) available.

• I1 is available from 9:00 AM - 1:00 PM on Day 1, and 10:00 AM - 2:00 PM on Day 2.
• I2 is available from 10:00 AM - 3:00 PM on Day 1, and 9:00 AM - 1:00 PM on Day 2.
• P1 must be interviewed before 11:00 AM on Day 1.
• P2 and P3 must be interviewed consecutively by the same interviewer.
• P4 requires I1.
• P5 cannot be interviewed after 1:00 PM on any day.
• P6 must be interviewed on Day 2.

What is the earliest time all 6 participants can be interviewed?

A sports club has 120 members. The following information is known about their preferences for three activities: Tennis, Swimming, and Gym.

- 60 members use the Gym.
- 40 members go Swimming.
- 30 members play Tennis.
- 10 members do both Swimming and Gym.
- 5 members do all three activities.
- No one does only Tennis and Swimming, and no one does only Tennis and Gym.

How many members do not participate in any of these three activities?

A delivery service charges based on parcel size and destination zone:

• Zone A: $$ \$5 $$
• Zone B: $$ \$8 $$
• Zone C: $$ \$12 $$

Additionally, parcels over $$ 10 \text{ kg} $$ incur an extra $$ \$3 $$ charge. Oversized parcels (length + width + height > $$ 150 \text{ cm} $$) incur an extra $$ \$5 $$ charge.

A parcel weighs $$ 8 \text{ kg} $$, has dimensions $$ 60 \text{ cm} \times 40 \text{ cm} \times 30 \text{ cm} $$, and is sent to Zone B. What is the total delivery cost?

A community library has set the following borrowing limits per member: Fiction: 6 books; Non-fiction: 4 books; Magazines: 2 items. Sarah currently has 4 fiction books, 1 non-fiction book, and 2 magazines on loan. How many more items in total can she borrow?

Four couriers (Xavier, Yolanda, Zander, and Wendy) are available to deliver packages to three different zones. The delivery times (in minutes) for each courier to each zone are shown in the table below:

The following constraints apply: Each courier can be assigned to only one zone. To meet demand, Zone 1 requires two couriers, while Zone 2 and Zone 3 each require one courier.

Determine the minimum total delivery time required for all four couriers to be assigned to these zones while satisfying the requirements.