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The provided solution refers to "Gold package" and "Economy package" costs based on "Time (n)" and "Cost (C)". It calculates fixed costs, cost per minute, and formulates equations for these packages.

Business/Management

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2.1.1

  1. Identify the fixed cost and cost per minute for the Gold package.

    From the table for the Gold package:
    When Time (nn) is 0 minutes, the Cost is R40. This is the fixed cost.
    When Time (nn) is 10 minutes, the Cost is R45.
    The increase in cost for 10 minutes is R45−R40=R5\text{R}45 - \text{R}40 = \text{R}5.

  2. Calculate the cost per minute.

    Cost per minute =Change in CostChange in Time=R510 minutes=R0.50 per minute= \frac{\text{Change in Cost}}{\text{Change in Time}} = \frac{\text{R}5}{10 \text{ minutes}} = \text{R}0.50 \text{ per minute}.

  3. Formulate the equation.

    The formula for the Gold package is Cost=Fixed Cost+(Cost per minute×n)\text{Cost} = \text{Fixed Cost} + (\text{Cost per minute} \times n).

    C=R40+R0.50×nC = \text{R}40 + \text{R}0.50 \times n

    The formula for calculating the Gold package is R40+R0.50×n\boxed{\text{R}40 + \text{R}0.50 \times n}.

    2.1.2

  4. Determine the value of A for the Economy package.

    The formula for the Economy package is given as C=R20+R1×nC = \text{R}20 + \text{R}1 \times n.
    From the table, A is the cost when n=30n=30 minutes.

    A=20+1×30A = 20 + 1 \times 30 A=20+30A = 20 + 30 A=50A = 50
  5. Determine the value of B for the Gold package.

    The formula for the Gold package is C=R40+R0.50×nC = \text{R}40 + \text{R}0.50 \times n.
    From the table, B is the cost when n=250n=250 minutes.

    B=40+0.50×250B = 40 + 0.50 \times 250 B=40+125B = 40 + 125 B=165B = 165

    The values are A=50 and B=165\boxed{A = 50 \text{ and } B = 165}.

    2.1.3

    To draw the graphs, we will plot points for each package and connect them with a straight line.
    Let nn be the time in minutes (x-axis) and CC be the cost in rands (y-axis).

    Economy Package (CE=20+nC_E = 20 + n):

    • (0, 20)
    • (10, 30)
    • (20, 40)
    • (30, 50)
    • (100, 120)
    • (250, 270)
    • (600, 620)

    Gold Package (CG=40+0.5nC_G = 40 + 0.5n):

    • (0, 40)
    • (10, 45)
    • (20, 50)
    • (30, 55)
    • (100, 90)
    • (250, 165)
    • (600, 340)

    Intersection Point:
    To find where the costs are equal, set CE=CGC_E = C_G:

    20+n=40+0.5n20 + n = 40 + 0.5n n−0.5n=40−20n - 0.5n = 40 - 20 0.5n=200.5n = 20 n=200.5n = \frac{20}{0.5} n=40 minutesn = 40 \text{ minutes}

    At n=40n=40 minutes, CE=20+40=60C_E = 20 + 40 = 60 and CG=40+0.5(40)=40+20=60C_G = 40 + 0.5(40) = 40 + 20 = 60.
    The intersection point is (40, 60).

    Graphing Instructions:

    1. Draw a set of axes. Label the x-axis "Time (minutes)" and the y-axis "Cost (Rands)".
    2. Choose an appropriate scale for both axes. For example, the x-axis can go from 0 to 600 (e.g., increments of 50 or 100), and the y-axis can go from 0 to 650 (e.g., increments of 50 or 100).
    3. Plot the points for the Economy package and draw a straight line through them. Label this line "Economy Package".
    4. Plot the points for the Gold package and draw a straight line through them. Label this line "Gold Package".
    5. Ensure both lines intersect at the point (40, 60).

    2.1.4

  6. Calculate the cost for the Economy package at 32 minutes.

    Using the formula CE=R20+R1×nC_E = \text{R}20 + \text{R}1 \times n:

    CE=20+1×32C_E = 20 + 1 \times 32 CE=20+32C_E = 20 + 32 CE=R52C_E = \text{R}52
  7. Calculate the cost for the Gold package at 32 minutes.

    Using the formula CG=R40+R0.50×nC_G = \text{R}40 + \text{R}0.50 \times n:

    CG=40+0.50×32C_G = 40 + 0.50 \times 32 CG=40+16C_G = 40 + 16 CG=R56C_G = \text{R}56
  8. Compare the costs and verify Mondli's argument.

    For 32 minutes:
    Economy package cost = R52
    Gold package cost = R56
    Since R52<R56\text{R}52 < \text{R}56, the Economy package is cheaper for 32 minutes.
    Therefore, Mondli's argument is incorrect\boxed{\text{incorrect}}.

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