H/GT Algebra II – worksheet “Break Even”
Algebra II Pre AP – Break Even Worksheet Name___________________________
1. Every time a plumber makes a house call he gets paid a flat fee of $50 plus $40 per hour. Every hour he works he uses approximately $80 worth of materials. Let “x” represent the number of hours worked, S(x) represent total sales, and C(x) represent total cost.
_______________________ a) Write a sales equation
_______________________ b) Write a cost equation
_______________________ c) What is the break-even point?
_______________________ d) Write a profit equation.
e) Sketch the graph
2. A car company fins that the equation that relates overall sales and cost are the following: units is cars produced and sold; sales and cost are measurements in thousands of dollars.
Sales = 15 x Units – 13 Cost = 8 x Units + 2
a) Sketch the graph
_______________________ b) What is the break-even point?
_______________________ c) Write a profit equation.
_______________________ d) What is the profit at 200 cars sold?
3. A telephone company charges a $2.50 connection fee and 15 cents a minute after the first minute. The call itself costs them the following: Cost = 0.20 x Minutes + 0.13
_______________________ a) Write a sales equation
b) Sketch the graph
_______________________ c) What is the break-even point?
_______________________ d) Write a profit equation.
4. Suppose your family is going to buy a new air conditioning unit. One brand costs $1800 to buy and $60 a month to operate. A more expensive brand costs $2600 to buy but only $50 a month to operate. Let “x” represent time in months, f(x) total spent for cheaper unit, and g(x) represent total spent for more expensive unit.
_______________________ a) Write a function for f(x)
_______________________ b) Write a function for g(x)
_______________________ c) Find f(100) and g(100).
What do these numbers tell you
about the costs of the units after
100 months?
_______________________ d) Find the break even point.
e) Sketch the graph
5. A particular brand of car with the normal engine costs $11000 to purchase and 22 cents per mile to drive. The same care with a fuel-injection engine costs $11300 to purchase, but only 20 cents per mile to drive. Let “x” represent the number of miles driven, f(x) represent total cost for the normal engine car, and g(x) represent total cost for the fuel-injection engine car.
_______________________ a) Write a function for f(x).
_______________________ b) Find f(1000), f(10000), and f(100000)
_______________________ c) Write a function for g(x)
_______________________ d) Find g(1000), g(10000), and
g(100000)
_______________________ e) What is the break even point?
f) Sketch the graph
6. In a certain mill the cost C in thousands of dollars of producing x tons of steel is given by [pic]. The revenue R in thousands of dollars from selling x tons is given by [pic].
_______________________ a) Find the break even point
_______________________ b) What does R(x) – C(x) measure for all x values greater than the break even
point?
7. Kroger and Randall’s are having a sale on Juice. Kroger is taking 40% off the original price and Randall’s is taking $1.50 off the original price.
_______________________ a) Find the break even point
_______________________ b) For what regular prices would Kroger’s sale be the better deal?
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