Question

Jason typically uses the Internet to buy various items. If the total cost of the items ordered, at one time, is \(\$ 200\) or more, then the shipping and handling is free; otherwise, the shipping and handling is \(\$ 10\) per item. Design an algorithm that prompts Jason to enter the number of items ordered and the price of each item. The algorithm then outputs the total billing amount. Your algorithm must use a loop (repetition structure) to get the price of each item. (For simplicity, you may assume that Jason orders no more than five items at a time.)

Short answer

The algorithm calculates costs with free shipping if the item total is $200 or more; otherwise, it charges $10 per item for shipping.

Step-by-step solution

Initialize Variables

Start by initializing a variable to store the total price of items before checking for shipping costs. Also, initialize a counter for the loop to track the number of items Jason orders.

Set Up User Input Loop

Create a loop that will run a fixed number of times (up to 5) to prompt Jason to enter the price of each item. Each time Jason enters a price, add this price to the total price variable.

Calculate Total Item Cost

Inside the loop, continuously update the total cost by adding each entered item price to the total cost variable.

Determine Shipping and Handling Cost

Once the loop has completed, check if the total item cost is $200 or more. If it is, set the shipping cost to $0; otherwise, multiply the number of items by $10 to calculate the shipping cost.

Calculate Total Billing Amount

Add the shipping and handling cost (determined in Step 4) to the total item cost to get the final total billing amount.

Output the Total Billing Amount

Display the final total billing amount, which includes the cost of the items and the applicable shipping fee, to Jason.

Key concepts

Repetition Structure

Repetition structures, commonly called loops, are an essential part of algorithm design. They allow us to perform a set of instructions repeatedly without having to write them out multiple times. In Jason's algorithm for calculating his billing, a loop is used to ask for and read the price of each item he intends to buy. By limiting the loop to 5 iterations, the algorithm ensures it considers every item ordered while remaining simple and efficient. This structure is beneficial as it automatically manages the repetition, updating the total price as each item is added.
Despite various types of loops such as `for`, `while`, and `do-while`, the algorithm chooses one that matches the condition of running a pre-set number of times, making `for` loops particularly suitable. By understanding how loops work, controlling, and knowing how and when to stop them, algorithm designers can create efficient solutions without redundant code.

User Input

User input is a critical part of interactive programs and algorithms. It allows the program to receive data from the user, which can then be used in computations. In the algorithm designed for Jason, user input is leveraged to get the precise price of each item he wants to purchase. This interaction is crucial because it personalizes the billing process and ensures the correct calculation by involving the user.
Once the loop starts, the algorithm prompts Jason for the price of each item. This makes the process interactive, where Jason has control over the input, leading to flexibility in the total billing outcome. Proper handling of user input involves guiding users on what data to enter and managing exceptions effectively. By prompting users accurately and validating the input, algorithms become robust and free from incorrect data entries.

Total Billing Calculation

The total billing calculation involves summing up the total price of items and applying any additional charges, such as shipping fees. At the algorithm's completion, the total billing amount is calculated by adding any additional costs to the sum of item prices. The process begins by calculating the total item cost in the loop, which is then checked against the free shipping threshold.
If Jason's total reaches or exceeds $200, he benefits from free shipping, making his costs limited to just the items he purchases. Conversely, if his total is less, a charge based on the number of items (\[10 imes ext{number of items ordered} \] formula) is added. This holistic approach to calculation ensures the final price Jason pays reflects all applicable charges reliably. Developing an algorithm with these considerations involves clear logic and understanding of conditional statements to decide what charges apply.