Assignment for economics
Content
2nd year Automotive and Locomotive Engineering
Engineering Economy and Management – Assignment # 3
1) Handheld fiber-optic meters with white light polarization interferometry are useful for
measuring temperature, pressure, and strain in electrically noisy environments. The fixed
costs associated with manufacturing are $800,000 per year. If a base unit sells for $2950
and its variable cost is $2075, (a) how many units must be sold each year for breakeven
( analytically and graphically) (b) what will the profit be for sales of 3000 units per year?
Solution
(a)
XBE = the break even quantity (units /year)
r = selling price per unit
v = variable cost per unit
XBE = F / (r – v) = 800,000 / (2950 – 2075) = 914 units per year
(b)
Profit (or loss) = TR – TC = r X – (F+ v X) = (2950 * 3000) – (800,000 + 2075
*3000) = $1,825,000 per year profit since it is positive
To Draw
X
0
1000
2000
TR
0
2950000
5900000
TC
800000
2875000
4950000
From the graph:
Xbe = 914
2) Nicholea Water LLC dispenses its product Nature’s Pure Water via vending machines
with most current locations at food markets and pharmacy or chemist stores. The average
monthly fixed cost per site is $900, while each gallon costs $0.18 to purify and sells for
$0.30. (a) Determine the monthly sales volume needed to break even (analytically and
graphically). (b) What will the profit be for sales of 7000 gallons per month?
Solution
The same as number 1
3) Consider the accompanying breakeven graph for an investment, and answer the following
questions as they pertain to the graph.
400000
350000
Total
Revenue
300000
250000
Dollars
200000
150000
100000
50000
0
0
250
500
750
1000
1250
1500
1750
Output (Units / Year)
a)
b)
c)
d)
Give the equation to describe total revenue for X units per year.
Give the equation to describe total costs for X units per year.
What is the "breakeven" level of X in terms of costs and revenues?
If you sell 1600 units this year, will you have a profit or loss? How much?
Solution
a)
At breakeven Xbe = 1000 units/year
2000
TC = TR = 200,000
Then TR = 200,000 = 1000*r
r = 200 $/unit
TR = 200 X
b) At breakeven Xbe = 1000 units/year TC = TR = 200,000
From the graph F = 100,000
TC = 200,000 = 100000 + 1000 * v
v = 100$/unit
TC = F + 100X
c) XBE = F / (r – v) = 100,000 / (200 – 100) = 1000 units per year
d) At X=1600 units /year
Profit (or loss) = TR – TC = r X – (F+ v X) = (200 * 1600) – (100,000 + 100
*1600) = $60,000 per year profit since it is positive
4) Quatro Hermanas, Inc. is investigating implementing some new production machinery as
part of its operations. Three alternatives have been identified, and they have the following
fixed and variable costs:
Alternative
Annual Fixed Cost ($)
Variable Cost per unit ($)
$120,000
$17
220,000
4
150,000
5.5
Determine the ranges of production (units produced per year) over which each alternative
would be recommended for implementation by Quatro Hermanas
A
B
C
Solve by drawing
5) Three alternative designs have been created by Snakisco engineers for a new machine that
spreads cheese between the crackers in a Snakisco snack. Each machine design has unique total
costs (fixed and variable) based on the annual production rate of boxes of these crackers. The
costs for the three designs are given (where Q is the annual production rate of boxes of cheese
crackers).
Design
A
B
C
Fixed Cost ($)
100,000
350,000
600,000
Annual Variable Cost ($)
20.5 Q
10.5 Q
8Q
Graphically, determine which of the machine designs would be recommended for different levels
of annual production of boxes of snack crackers. Management is interested in the production
interval of 0-150,000 boxes of crackers per year. Over what production volume would each
design (A or B or C) be chosen?
Solve by drawing
6) Samsung Electronics is trying to reduce supply chain risk by making more responsible
make-buy decisions through improved cost estimation. A high-use component (expected
usage is 5000 units per year) can be purchased for $25 per unit with delivery promised
within a week. Alternatively, Samsung can make the component in-house and have it
readily available at a cost of $5 per unit, if equipment costing $150,000 is purchased.
Labor and other operating costs are estimated to be $35,000 per year over the study
period of 5 years. Salvage is estimated at 10% of first cost and i =12% per year. Neglect
the element of availability (a) to determine the breakeven quantity and (b) to recommend
making or buying at the expected usage level.
Solution
(a) Solve the relation AWbuy = AWmake for Q = number of units per year.
-25Q = -150,000(A/P,12%,5) + 15,000(A/F,12%,5) – 35,000 – 5Q
-20Q = -150,000(0.27741) + 15,000(0.15741) – 35,000
Q = -74,250/-20
= 3713 units per year
(b) Since 5000 > 3713, select the make option. It has the smaller slope of 5 versus
25 for the buy option.
7) An irrigation canal contractor wants to determine whether he should purchase a used
Caterpillar mini excavator or a Toro powered rotary tiller for servicing irrigation ditches
in an agricultural area of California. The initial cost of the excavator is $26,500 with a
$9000 salvage value after 10 years. Fixed costs for insurance, license, etc. are expected to
be $18,000 per year. The excavator will require one operator at $15 per hour and
maintenance at $1 per hour. In 1 hour, 0.15 mile of ditch can be prepared. Alternatively,
the contractor can purchase a tiller and hire 2 workers at $11 per hour each. The tiller
costs $1200 and has a useful life of 5 years with no salvage value. Its operating cost is
expected to be $1.20 per hour, and with the tiller, the two workers can prepare 0.04 mile
of ditch in 1 hour. The contractor’s MARR is 10% per year. Determine the number of
miles of ditch per year the contractor would have to service for the two options to break
even.
Solution
VCexcavator = (15 + 1)/0.15 = $106.67 per mile
VCtiller = [2(11) + 1.20]/0.04 = $580 per mile
FCexcavator = -26,500(A/P,10%,10) – 18,000 + 9,000(A/F,10%,10)
= -26,500(0.16275) – 18,000 + 9,000(0.06275)
= $-21,748 per year
FCtiller = -1200(A/P,10%,5)
= -1200(0.26380)
= $-316.56 per year
Equate the AW relations and let x = breakeven miles per year
-21,748 – 106.67x = -316.56 – 580x
x = 45.3 miles per year
Engineering Economy and Management – Assignment # 3
1) Handheld fiber-optic meters with white light polarization interferometry are useful for
measuring temperature, pressure, and strain in electrically noisy environments. The fixed
costs associated with manufacturing are $800,000 per year. If a base unit sells for $2950
and its variable cost is $2075, (a) how many units must be sold each year for breakeven
( analytically and graphically) (b) what will the profit be for sales of 3000 units per year?
Solution
(a)
XBE = the break even quantity (units /year)
r = selling price per unit
v = variable cost per unit
XBE = F / (r – v) = 800,000 / (2950 – 2075) = 914 units per year
(b)
Profit (or loss) = TR – TC = r X – (F+ v X) = (2950 * 3000) – (800,000 + 2075
*3000) = $1,825,000 per year profit since it is positive
To Draw
X
0
1000
2000
TR
0
2950000
5900000
TC
800000
2875000
4950000
From the graph:
Xbe = 914
2) Nicholea Water LLC dispenses its product Nature’s Pure Water via vending machines
with most current locations at food markets and pharmacy or chemist stores. The average
monthly fixed cost per site is $900, while each gallon costs $0.18 to purify and sells for
$0.30. (a) Determine the monthly sales volume needed to break even (analytically and
graphically). (b) What will the profit be for sales of 7000 gallons per month?
Solution
The same as number 1
3) Consider the accompanying breakeven graph for an investment, and answer the following
questions as they pertain to the graph.
400000
350000
Total
Revenue
300000
250000
Dollars
200000
150000
100000
50000
0
0
250
500
750
1000
1250
1500
1750
Output (Units / Year)
a)
b)
c)
d)
Give the equation to describe total revenue for X units per year.
Give the equation to describe total costs for X units per year.
What is the "breakeven" level of X in terms of costs and revenues?
If you sell 1600 units this year, will you have a profit or loss? How much?
Solution
a)
At breakeven Xbe = 1000 units/year
2000
TC = TR = 200,000
Then TR = 200,000 = 1000*r
r = 200 $/unit
TR = 200 X
b) At breakeven Xbe = 1000 units/year TC = TR = 200,000
From the graph F = 100,000
TC = 200,000 = 100000 + 1000 * v
v = 100$/unit
TC = F + 100X
c) XBE = F / (r – v) = 100,000 / (200 – 100) = 1000 units per year
d) At X=1600 units /year
Profit (or loss) = TR – TC = r X – (F+ v X) = (200 * 1600) – (100,000 + 100
*1600) = $60,000 per year profit since it is positive
4) Quatro Hermanas, Inc. is investigating implementing some new production machinery as
part of its operations. Three alternatives have been identified, and they have the following
fixed and variable costs:
Alternative
Annual Fixed Cost ($)
Variable Cost per unit ($)
$120,000
$17
220,000
4
150,000
5.5
Determine the ranges of production (units produced per year) over which each alternative
would be recommended for implementation by Quatro Hermanas
A
B
C
Solve by drawing
5) Three alternative designs have been created by Snakisco engineers for a new machine that
spreads cheese between the crackers in a Snakisco snack. Each machine design has unique total
costs (fixed and variable) based on the annual production rate of boxes of these crackers. The
costs for the three designs are given (where Q is the annual production rate of boxes of cheese
crackers).
Design
A
B
C
Fixed Cost ($)
100,000
350,000
600,000
Annual Variable Cost ($)
20.5 Q
10.5 Q
8Q
Graphically, determine which of the machine designs would be recommended for different levels
of annual production of boxes of snack crackers. Management is interested in the production
interval of 0-150,000 boxes of crackers per year. Over what production volume would each
design (A or B or C) be chosen?
Solve by drawing
6) Samsung Electronics is trying to reduce supply chain risk by making more responsible
make-buy decisions through improved cost estimation. A high-use component (expected
usage is 5000 units per year) can be purchased for $25 per unit with delivery promised
within a week. Alternatively, Samsung can make the component in-house and have it
readily available at a cost of $5 per unit, if equipment costing $150,000 is purchased.
Labor and other operating costs are estimated to be $35,000 per year over the study
period of 5 years. Salvage is estimated at 10% of first cost and i =12% per year. Neglect
the element of availability (a) to determine the breakeven quantity and (b) to recommend
making or buying at the expected usage level.
Solution
(a) Solve the relation AWbuy = AWmake for Q = number of units per year.
-25Q = -150,000(A/P,12%,5) + 15,000(A/F,12%,5) – 35,000 – 5Q
-20Q = -150,000(0.27741) + 15,000(0.15741) – 35,000
Q = -74,250/-20
= 3713 units per year
(b) Since 5000 > 3713, select the make option. It has the smaller slope of 5 versus
25 for the buy option.
7) An irrigation canal contractor wants to determine whether he should purchase a used
Caterpillar mini excavator or a Toro powered rotary tiller for servicing irrigation ditches
in an agricultural area of California. The initial cost of the excavator is $26,500 with a
$9000 salvage value after 10 years. Fixed costs for insurance, license, etc. are expected to
be $18,000 per year. The excavator will require one operator at $15 per hour and
maintenance at $1 per hour. In 1 hour, 0.15 mile of ditch can be prepared. Alternatively,
the contractor can purchase a tiller and hire 2 workers at $11 per hour each. The tiller
costs $1200 and has a useful life of 5 years with no salvage value. Its operating cost is
expected to be $1.20 per hour, and with the tiller, the two workers can prepare 0.04 mile
of ditch in 1 hour. The contractor’s MARR is 10% per year. Determine the number of
miles of ditch per year the contractor would have to service for the two options to break
even.
Solution
VCexcavator = (15 + 1)/0.15 = $106.67 per mile
VCtiller = [2(11) + 1.20]/0.04 = $580 per mile
FCexcavator = -26,500(A/P,10%,10) – 18,000 + 9,000(A/F,10%,10)
= -26,500(0.16275) – 18,000 + 9,000(0.06275)
= $-21,748 per year
FCtiller = -1200(A/P,10%,5)
= -1200(0.26380)
= $-316.56 per year
Equate the AW relations and let x = breakeven miles per year
-21,748 – 106.67x = -316.56 – 580x
x = 45.3 miles per year
