Problem 6 - Basic Engineering Mathematics

Question

The retail price of a product costing \(£ 2\) is made up as follows: materials \(10 \mathrm{p}\), labour \(20 \mathrm{p}\), research and development \(40 \mathrm{p}\), overheads \(70 \mathrm{p}\), profit \(60 \mathrm{p}\). Present these data on a pie diagram.

Step-by-Step Solution

Answer

Materials 5%, Labour 10%, Research and Development 20%, Overheads 35%, Profit 30% are the sectors of the pie chart.

Step 1: Understand the components

The retail price is composed of different components. For this problem, the components are: materials (10p), labor (20p), research and development (40p), overheads (70p), and profit (60p). Since 1 pound (£) equals 100 pence (p), we convert all components into pence: 10p + 20p + 40p + 70p + 60p = 200p.

Step 2: Calculate the percentage of each component

Each component should be represented as a percentage of the total retail price (200p). Calculate as follows:1. Materials: \(\frac{10}{200} \times 100 = 5\%\)2. Labour: \(\frac{20}{200} \times 100 = 10\%\)3. Research and Development: \(\frac{40}{200} \times 100 = 20\%\)4. Overheads: \(\frac{70}{200} \times 100 = 35\%\)5. Profit: \(\frac{60}{200} \times 100 = 30\%\).

Step 3: Create the pie chart

Plot each percentage as a sector in a pie chart: - Materials: 5% - Labour: 10% - Research and Development: 20% - Overheads: 35% - Profit: 30% Each section of the pie chart should be proportional to its percentage. You can use a drawing tool or software to create this representation.

Key Concepts

Percentage Calculation

Calculating percentages is a straightforward but essential skill, especially when it comes to breaking down costs. To determine the percentage that each cost component contributes to the total retail price of a product, you follow a simple formula. First, take the individual cost of each component and divide it by the total retail cost. This fraction then needs to be multiplied by 100 to convert it into a percentage.
For instance, for materials that cost 10p in a product costing a total of 200p, you calculate as follows:

• Materials: \( \frac{10}{200} \times 100 = 5\% \)
• This means that materials comprise 5% of the total cost.

Understanding this calculation helps you efficiently categorize and understand each component's financial weight within the overall cost. Refining accuracy in percentage calculation ensures precise data interpretation and reporting.

Data Visualization

Visualizing data with pie charts takes numbers and transforms them into an easy-to-understand picture. Pie charts are circular charts divided into sectors, each representing a proportion of the whole. In the case of cost breakdown, each sector corresponds to a different cost component of a product.
When you draw a pie chart to represent the different components, the size of each segment is determined by the component's percentage of the total. This offers a visual intuition into how each component contributes to the full retail price.

• A segment representing overheads would cover 35% of the circle.
• The profit section would get 30% of the pie.

Leveraging pie charts is one of the most effective data visualization methods for quickly communicating how explicit costs relate to one another and to the total sum. It simplifies complex data into an easily digestible format.

Cost Components

Breaking down the cost components of a product helps to understand where the money is going. In this exercise, you have components such as materials, labor, research and development, overheads, and profit. Each of these plays a vital role in the formation of the retail price.
Understanding these components in detail:

• Materials: Basic raw materials required to produce the product.
• Labour: The cost of hiring staff to produce or service the product.
• Research and Development: Investments into the innovation and improvement of the product.
• Overheads: Indirect costs such as utilities and rent.
• Profit: The money earned after all expenses are considered.

By deeply analyzing these components, businesses and customers both attain clarity on what factors drive pricing and to what extent, promoting informed decision-making.