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Consider a business that sells burgers. The selling price of each burger is R30.00. The fixed costs are R120.00 and the cost to make one burger is R10.00. A) Determine the formula for Income and Expen

Mathematics

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here are the solutions to the questions:

2.3.1

  1. Determine the formula for Income and Expense.

    • Income (R) = Number of burgers sold ×\times R30.0030.00
    • Expense (R) = Fixed costs + (Number of burgers sold ×\times Cost to make one burger) Expense (R) = R120.00120.00 + (Number of burgers sold ×\times R10.0010.00)
  2. Calculate the value for A (Income when 4 burgers are sold).

    Income for 4 burgers=4×R30.00\text{Income for 4 burgers} = 4 \times \text{R}30.00 Income for 4 burgers=R120.00\text{Income for 4 burgers} = \text{R}120.00

    So, A = 120\boxed{\text{120}}.

  3. Calculate the value for B (Expense when 6 burgers are sold).

    Expense for 6 burgers=R120.00+(6×R10.00)\text{Expense for 6 burgers} = \text{R}120.00 + (6 \times \text{R}10.00) Expense for 6 burgers=R120.00+R60.00\text{Expense for 6 burgers} = \text{R}120.00 + \text{R}60.00 Expense for 6 burgers=R180.00\text{Expense for 6 burgers} = \text{R}180.00

    So, B = 180\boxed{\text{180}}.

    The completed table is:

    Number of burgers sold0246810
    Income (R)060120180240300
    Expense (R)120140160180200220

    2.3.2

  4. Identify the coordinates for plotting the Income and Expense graphs.

    • Income (Number of burgers, Income in R): (0, 0), (2, 60), (4, 120), (6, 180), (8, 240), (10, 300)
    • Expense (Number of burgers, Expense in R): (0, 120), (2, 140), (4, 160), (6, 180), (8, 200), (10, 220)
  5. Draw the graphs on a set of axes.

    Plot the income points and draw a line through them.
    Plot the expense points and draw a line through them.
    (Note: As an AI, I cannot draw the graph for you, but you can plot these points on graph paper.)

  6. Determine the break-even point from the graph.

    The break-even point is where the Income graph and the Expense graph intersect. At this point, Income equals Expense.
    From the table in 2.3.1, when 6 burgers are sold, both Income and Expense are R180.
    Therefore, the break-even point is (6 burgers, R180)\boxed{\text{(6 burgers, R180)}}.

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