Worksheet: Investigating Profits

In this worksheet, we will practice using functions and systems of equations to investigate the profits of a manufacturer.

Q1:

A stuffed animal business has a cost function of 𝐶=12𝑥+30 and a revenue function 𝑅=20𝑥. First, find the break-even point. Then, calculate the corresponding revenue.

  • A 𝑥 = 7 5 , 𝑅 = 1 5 4
  • B 𝑥 = 0 , 𝑅 = 7 5
  • C 𝑥 = 7 5 , 𝑅 = 0
  • D 𝑥 = 1 5 4 , 𝑅 = 7 5

Q2:

A guitar factory has a cost of production given by 𝐶(𝑥)=75𝑥+50,000. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Give your answer to the nearest dollar.

  • A $ 4 0 9
  • B $ 6 6 6
  • C $ 4 0 8
  • D $ 6 6 7

Q3:

A musician charges 𝐶(𝑥)=$(64𝑥+20,000), where 𝑥 is the total number of attendees at the concert. The venue charges $80 per ticket. After how many sold tickets does the venue break even, and what is the value of the total tickets sold at that point?

  • A139 tickets, $11,120
  • B2,000 tickets, $160,000
  • C1,500 tickets, $116,000
  • D1,250 tickets, $100,000

Q4:

A cell phone factory produces 𝑥 cellphones with cost 𝐶(𝑥)=150𝑥+10,000 and revenue 𝑅(𝑥)=200𝑥. What is the breakeven point?

  • A 𝑥 = 2 0 0 7
  • B 𝑥 = 1 0 0 7
  • C 𝑥 = 2 0 0
  • D 𝑥 = 4 0 , 0 0 0
  • E 𝑥 = 0

Q5:

A fast-food restaurant has a cost of production 𝐶(𝑥)=11𝑥+120 and a revenue function 𝑅(𝑥)=5𝑥. When does the company start to turn a profit?

  • Anever
  • Bwhen 𝑥=100
  • Cwhen 𝑥=7.5
  • Dwhen 𝑥=20

Q6:

A laptop company has discovered that their cost and revenue functions for each day are 𝐶(𝑥)=3𝑥10𝑥+200 and 𝑅(𝑥)=2𝑥+100𝑥+50. Find the maximum and minimum number of laptops they could produce each day while still making a profit.

Hint: Your answers should be integers.

  • Aminimum: 2 laptops, maximum: 20 laptops
  • Bafter 51 computers
  • Cminimum: 2 laptops, maximum: 21 laptops
  • Dminimum: 1 laptop, maximum: 21 laptops

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