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Cost Calculations and Profit Analysis in Business Scenarios

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Explore the concepts of cost calculation and profit analysis in shipping and bus company scenarios. Understand how to determine costs, profits, rules, and break-even points in various situations.

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Cost Calculations and Profit Analysis in Business Scenarios

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  1. Bell Work • A shipping company charges a fixed fee and an amount per kg of weight. • John ships a 5 kg package for $16.50 and Sarah ships a 10 kg package for $26.50. • How much will it cost you to ship a 15kg package using the same company?

  2. A bus company makes $45 in profit if 20 people are on the bus and $130 in profit if 30 people are on the bus. • What it the rule used to calculate the profit? • What does the initial value represent? • How many people need to be on the bus to break even?

  3. Answers pg 112-118

  4. Page 112 • 1a) constant b) partial c) other d) direct e) partial f) other 2a) partial b) direct c) other d) constant b) partial d) constant

  5. Page 113 • 3a) partial b) constant c) direct • d) other e) other f) partial 4a) constant b) direct c) other d) Partial 5a) y -2, 0, 2 b) y -1, 1, 3 c) y 3, 0, -3

  6. Page 114 and 115 • On overhead

  7. Page 116 • 8 a) 650 650 650 650 …. B) y = 650 C) 0 D) parallel to x axis E) constant • 9 b) Variables are proportional C) 45$ per person D) straight line that starts at the origin E) Direct F) [0, 40] called the domain b) [0, 1800] called the range G) it also increases

  8. Page 117 • 10 b) no • C) 1) 0.03 per page • 2) 5$ • 3) y = 0.03x + 5 • D) straight line that does not pass through the origin • E) Partial • F) [0, 400] domain 2) [5, 17] Range • G) it also increases • H) 175 pages 2) 223 pages

  9. Page 117 and 118 • 11a) 1. $75/chair 2. $-3000 3. y = 75 x – 3000 (x is the number of chairs and y is the net profit) b) 1. [0, 100] 2. [-3000, 4500] c) 1. [40, 100] 2. [0, 40[ d) it increases e) 40 chairs (set y equal to 0 and solve 0 = 75x – 3000) f) 48 chairs 2. 62 chairs (replace y with 600 and then 1650)

  10. Page 118 • 12 • A) -3600 per year • This is how much the value decreases per year • B) $24 000 • C) y = -3600 + 24 000 (y is the value, x is the number of years) • D) 9600 (replace x with 4) • E) 2.5 years 2. 6 years (replace y with these amounts) • F) after 6 years and 8 months (set y = 0 and solve 6.6666 6 and 2/3  6 years and 8 months) • G) 1. [0, 6 and 2/3] 2. [0, 24 000] • H) it decreases • i) straight line the crosses the y axis at 24000 and the x axis at 6 and 2/3.

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