This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Welcome back xhlovomkasi — missed you this week. Here are the solutions to your questions. 2.1.1 Step 1: Identify the fixed cost and cost per minute for the Gold package. From the table for the Gold package: When Time (n) is 0 minutes, the Cost is R40. This is the fixed cost. When Time (n) is 10 minutes, the Cost is R45. The increase in cost for 10 minutes is R45 - R40 = R5. Step 2: Calculate the cost per minute. Cost per minute = Change in CostChange in Time = R510 minutes = R0.50 per minute. Step 3: Formulate the equation. The formula for the Gold package is Cost = Fixed Cost + (Cost per minute × n). C = R40 + R0.50 × n The formula for calculating the Gold package is R40 + R0.50 × n. 2.1.2 Step 1: Determine the value of A for the Economy package. The formula for the Economy package is given as C = R20 + R1 × n. From the table, A is the cost when n=30 minutes. A = 20 + 1 × 30 A = 20 + 30 A = 50 Step 2: Determine the value of B for the Gold package. The formula for the Gold package is C = R40 + R0.50 × n. From the table, B is the cost when n=250 minutes. B = 40 + 0.50 × 250 B = 40 + 125 B = 165 The values are A = 50 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 n be the time in minutes (x-axis) and C be the cost in rands (y-axis). Economy Package (C_E = 20 + n): • (0, 20) • (10, 30) • (20, 40) • (30, 50) • (100, 120) • (250, 270) • (600, 620) Gold Package (C_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 C_E = C_G: 20 + n = 40 + 0.5n n - 0.5n = 40 - 20 0.5n = 20 n = (20)/(0.5) n = 40 minutes At n=40 minutes, C_E = 20 + 40 = 60 and C_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 Step 1: Calculate the cost for the Economy package at 32 minutes. Using the formula C_E = R20 + R1 × n: C_E = 20 + 1 × 32 C_E = 20 + 32 C_E = R52 Step 2: Calculate the cost for the Gold package at 32 minutes. Using the formula C_G = R40 + R0.50 × n: C_G = 40 + 0.50 × 32 C_G = 40 + 16 C_G = R56 Step 3: Compare the costs and verify Mondli's argument. For 32 minutes: Economy package cost = R52 Gold package cost = R56 Since R52 < R56, the Economy package is cheaper for 32 minutes. Therefore, Mondli's argument is incorrect. What's next? Send 'em! 📸