The table shows the cost of manufacturing various quantities...

The table shows the cost of manufacturing various quantities of an item and the revenue obtained from their sale. $$\begin{array}{r|r|r|r|r|r|r|r|r|r}\hline \text { Quantity } & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 \\ \hline \text { cost (S) } & 120 & 400 & 600 & 780 & 1000 & 1320 & 1800 & 2500 & 3400 \\\hline \text { Revenue (S) } & 0 & 300 & 600 & 900 & 1200 & 1500 & 1800 & 2100 & 2400 \\\hline \end{array}$$ (a) What range of production levels appears to be profitable? (b) Calculate the profit or loss for each of the quantities shown. Estimate the most profitable production level.

The table shows the cost of manufacturing various quantities of an item and the revenue obtained from their sale.
$$\begin{array}{r|r|r|r|r|r|r|r|r|r}\hline \text { Quantity } & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 \\
\hline \text { cost (S) } & 120 & 400 & 600 & 780 & 1000 & 1320 & 1800 & 2500 & 3400 \\\hline \text { Revenue (S) } & 0 & 300 & 600 & 900 & 1200 & 1500 & 1800 & 2100 & 2400 \\\hline \end{array}$$
(a) What range of production levels appears to be profitable?
(b) Calculate the profit or loss for each of the quantities shown. Estimate the most profitable production level.

Key Concepts

Profit Calculation

Profit calculation involves subtracting the total cost from the total revenue to determine the net gain or loss for a given level of production. This concept is fundamental in assessing the financial outcome of business activities.

Cost Analysis

Cost analysis examines the expenses incurred in the process of manufacturing or providing a service. It involves understanding both fixed and variable costs which are crucial for making informed production and pricing decisions.

Revenue Analysis

Revenue analysis focuses on examining the income generated from sales. It helps in understanding how changes in production levels affect overall earnings, and is vital for evaluating business performance.

Break-even Analysis

Break-even analysis identifies the point where total revenue equals total cost, meaning the business is neither making a profit nor a loss. This concept is important for understanding the minimum performance required for profitability.

Production Optimization

Production optimization involves analyzing different production levels to determine which one generates the highest profit. This process requires comparing profit outcomes across various production quantities and selecting the optimal level to maximize financial performance.

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