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.

0 250 500 750 1000 1250 1500 1750 20000

50000

100000

150000

200000

250000

300000

350000

400000

Output (Units / Year)

Dol

lars

Total Cost

a) Give the equation to describe total revenue for X units per year.b) Give the equation to describe total costs for X units per year.c) What is the "breakeven" level of X in terms of costs and revenues?d) If you sell 1600 units this year, will you have a profit or loss? How much?

Solution

a)

At breakeven Xbe = 1000 units/year

TC = TR = 200,000

Total Revenue

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 yeard) 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:

Alternativ

eAnnual Fixed Cost ($)

Variable Cost per unit

($)

A $120,000 $17

B 220,000 4

C 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

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).

Desig

nFixed Cost ($) Annual Variable Cost ($)

A 100,000 20.5 Q

B 350,000 10.5 Q

C 600,000 8 Q

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 versus25 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 mileVCtiller = [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 – 580xx = 45.3 miles per year