Problems with (*) are important
Problems with (**) are
harder or higher level
Problems with (B) are bonuses
PART (A): Cost, Revenue & Profit
- 1) A small home business is set up with an investment of
$10,000 for equipment. The business manufactures a
product at a cost of $0.65 per unit. If the product sells
for $1.20, how many units must be sold before the
business breaks even?
- 2) A person setting up a part-time business makes an
initial investment of $5,000. The unit cost of the
product is $21.60, and the selling price is $34.10.
- a) Find equations for the total cost C and total revenues
R for x units.
- b) Find the break-even point.
- 3) A manufacturing company determines the total cost in
dollars of producing x units of a certain product
is $25 per unit plus a fixed cost of $3500. Find the
equation of the cost, graph it, find the y-intercept and
- *4) In a manufacturer, the cost of producing 20
flashlights per week is $200 while the cost of producing
100 flashlights per week is $600.
- a) Find the equation for the cost.
- b) Find the cost of producing 150 flashlights per week.
- c) What is the manufacturer fixed cost?
- *5) A contractor purchases a piece of equipment for
$26,500. The equipment requires an average expenditure of
$5.25 per hour for fuel and maintenance, and the operator
is paid $9.50 per hour.
- a) Find a linear equation giving the total cost C
of operating this equipment t hours.
- b) Given that customers are charged $25 per hour of
machine use, write an equation for the revenue R derived
from t hours of use.
- c) Use the formula (P=R-C) to write an equation for the
profit derived from t hours of use.
- d) Find the number of hours the equipment must be
operated for the contractor to break even.
- 6) Suppose the cost for a product is $2.50 per unit with
a fixed cost of $1200. If the selling price per unit is
$10, how many units must be produced to break even?
(graph the equations and show the intersection point)
- B7) Use the data in the table below to solve the
following problem. (R-value of insulation is a measure
of its ability to resist heat transfer, higher R-value
means higher insulation)
- a) Write linear equations relating the R-value to the
thickness in inches for fiberglass insulation and
- b) Use the costs per cubic inch to determine which
product costs less and provides an R-value of 24.
||Cost/cubic inch $
- 8) A manufacturer sells belts for $12 per unit. The fixed
costs are $1600 per month, and the variable costs are $ 8
per unit. a) Write the equations of the revenue and the
cost function. b) Find the break-even point.
- *9) The total cost per week of producing a calculator is
C = 360 + 10x + 0.2x2. If
the price per unit sold is 50 - 0.2x, at what
level of production will the break even point(s) occur?
graph the problem.
- 10) A manufacturer determines that the revenue generated
by selling x units of a product is a linear
function of x. If the revenue from 20 units is
$380 and the revenue from 15 units is $285, find the
- 11) The Green-Belt Company determines that the cost of
manufacturing men's belts is $2 each plus $300 per day in
fixed costs. The company sells the belts for $3 each.
What is the break-even point? graph the problem.
- *12) Scott wants to buy a total of 500 shares in the
stock market. He will buy x shares at $4 per share and
the rest at $6 per share. Write the equation for the
total cost of the shares. What will be Scott's cost if he
buys 200 shares at $4 ?
- *13) The manager of a pie shop sells his pies for $6.5.
The overhead is $378 per day and each pie costs $1.10 to
- a) Write the revenue function, the cost function and the
- b) Write the marginal revenue, cost and profit function.
- c) Find the break even point.
- 14) A manufacturer of golf clubs finds that the fixed
costs are $5780 per week and the cost of producing each
set is $73.00. Each set of clubs can be sold for $243.00.
- a) Write the revenue function and the cost function.
- b) Write the profit function and the marginal profit
- c) Find the break even point.
- 15) A grocery store bought ice cream for 59 cents per
quart and stored them in two freezers. During the night,
one freezer "defrosted" and ruined 14 quarts.
If the remaining ice cream was sold for 98 cents per
quart, find the function for the profit in terms of the
number of quart bought.
- *16) The quantity sold x of a certain kind of
radio is inversely proportional to the price p. It
was found that 240,000 radios will be sold when the price
per radio is $12.50. How many will be sold if the price
- *17) The time t required to do a certain job
varies inversely as the number of people P who
work on the job. It takes 4 hours for 12 people to erect
some football bleacher. Find the variation constant and
how long would it take 3 people to do the same job?
- *18) The amount of garbage G produced in the United
states varies directly as the number of people N who
produce the garbage. It is known that 50 tons of garbage
is produced by 200 people in 1 year. The population in
San Francisco is 705,000. Find the variation constant and
the amount of garbage produced in San Francisco in 1
- 19) A bicycle manufacturer has a fixed cost of $500 per
week and a variable cost of $30 per bicycle. The
manufacturer sells the bicycles for $80 each.
- a) Find the cost function C(x), the revenue
- b) Find the profit function P(x).
- c) Find the output levels x at which P(x)
is positive . Graph the functions.
- *20) A lawnmower manufacturer sells mowers to a certain
retailer for $200 each, plus a handling charge of $75 on
each order. The retailer applies a markup of 40% to the
total price paid for the manufacturer.
- a) Find the function C giving the retailer's total
cost of a single order x lawnmowers.
- b) Find the function R giving the retailer's total
revenues from the sale.
- c) If the retailer sells all these lawnmower at the same
price, what is the retail price per lawnmower?
- 18,182 units
- a) C = 21.6x + 5000, R = 34.1x,
b) 400 units
- C=25x + 3500, y-intercept = 3500 , slope = 25
- a) C(x)= 5x + 100,
c) $100 per week
- a) C = 14.75t + 26,500
c) P = 10.25t - 26,500
d) 2585.4 hours
- 160 units
- a) R=3.2t-0.2, R = 3.6t + 0.4
b) fiberglass $ 1.58, cellulose $ 2.16
- a) R = 12x; C = 8x + 1600
b) 400 units
- at x = 10 and at x = 90
- R = 19 x
- x = 300 belts.
- C = 3000 - 2x, $ 2600.
- a) R = 6.50x, C = 1.10x + 378. P = 5.40x -378
b) 6.50; 1.10; 5.40 .
c) x = 70 pies.
- a) R = 243x, C = 73x + 5780
b) P = 170x - 5780; marginal prof. 170
c) x = 34 sets.
- P(x) = 0.39x - 13.72
- k = 48, t=16 hours.
- k = 0.25, G = 176,250 tons
- a) C(x)= 500 + 30x, R(x) = 80x,
b) P(x) = 50x - 500,
c) x > 10
- a) C(x)=200x + 75,
b) R(x)=280x + 105,
c) Pr(x)=280 + 105/x