a) For this situation, determine the volume of

optimal monthly sales of this product, and

calculate the profit (or loss) with the volume
optimal.
b) What is the range of the demand generated
utilities over a month?
A company manufactures and sells a product
of consumption, and has been sufficiently capable of
control the volume of the product with the variation
from the selling price. The company wishes to maximize
its net utility. It has concluded that the
relationship between price and demand, by month, is
approximates to D=500−5p, where p is the price
unit, in dollars. The fixed cost is $1,000 per month,
and the variable cost is $20 per unit. Respond
the following questions, both in an analytical form
as a graph: (2.3)
a) What is the optimal number of units that
should be produced and sold per month?
b) What is the maximum profit per month?
c) What are the equilibrium quantities of the
sales (range of demand volume that
generate profits)?
2.12.A company determined that the price and the
monthly demand for one of its products is
related by the equation
where is the unit price in dollars, and give the
monthly demand. The associated fixed costs are
$1,125/month, and the variable costs are $100/unit.
(2.3)
a) How many units need to be produced and sold?
every month to maximize profit?
b) How to know that the answer to the previous item
maximize utility?
c) Which of the following values of D represents
the break-even point? Why? i.10 units.
15 units.
units.
2.13. A place to deposit solid waste
of a city must be located in the site Ao in the
siteB. After being selected, some waste
solids will be transported to a plant of
electric energy that will be used as fuel.
The data for the transport of such waste
from each of the sites to the plant of
energy is presented in table P2.13.
a) If the power plant is going to pay $8.00 for each
cubic yard of selected solid waste
that they take her away, where should I
locate the garbage dump? Adopt the
point of view of the city and suppose that only
200,000 will be transported over the course of a year.
cubic yards of waste to the plant. Must
choose a site.
b) In relation to the power plant, the
cost in dollars per hour to produce electricity
esY=12 + 0.3X + 0.27X2, where X is
in megawatts. The income in dollars per
the hour for the sale of energy is 15X–
0.2X2. Find the value of X that yields the profit.
maximum. (2.3)
A plant has a manufacturing capacity to produce
4,100 hydraulic pumps per month. The
fixed cost is $504,000 per month. The variable cost
it is $166 per pump, and the selling price is
$328 per pump. (Assume that sales are
equal to the production volume). What is the
break-even point in the number of pumps
per month? What will be the percentage reduction?
What will happen at the break-even point if the costs
fixed costs decrease by 18% and variable costs
unit prices at 6%? (2.3)
2.15.Suppose that Corporation ABC has a
production (and sales) capacity of $1,000,000
per month. Its fixed costs (in a considerable range
the volume) is $350,000 per month, and the costs
variables are $0.50 per dollar of sales. (2.3)
a) What is the annual breakeven point of the volume
(D')? Build (graph) the graph of
balance.
b) What effect would the decrease have on D'?
variable cost per unit at 25% if consequently
Do fixed costs increase by 10%?
SECTION 2.8 / PROBLEMS 63
SiteA SiteB
4 miles 3 miles
$5,000 $100,000
Transportation cost $1.50/yd3-mile
Table P2.13 Table for problem 2.13
c) What would be the effect on D if fixed costs
would decrease by 10% and the variable cost by
Will the unit increase by the same percentage?
A company produces and sells a product
for the consumer and is able to control their demand
varying the selling price. The relationship
approximately between the price and the demand is
Where is the price per unit, in dollars, and D
it is the demand per month. The company seeks to maximize
its utility. The fixed cost is $1,000 per
month and the variable (cv) is $40 per unit. (2.3)
a) What is the number of units that must
to be produced and sold every month with the purpose of
to maximize utility?
b) Prove that the answer to the previous item
maximize utility.
A local defense contractor is thinking
to produce fireworks, as a way
to reduce their dependence on the military. The
Variable cost per unit is $40. The fixed cost
what can be assigned to the production of fires
artificial is despicable. The price that will be charged
per unit will be determined by the equation
p = $180 - 5D, where D represents the demand,
in units sold per week. (2.3)
a) What is the optimal number of units that
the contractor must produce with the aim of
maximize utility per week?
b) What is the usefulness if the number is produced
optimal units?
2.18. An operating plant has fixed costs of
$2,000,000 per year, and its production capacity
it is 100,000 electrical devices per year. The cost
the variable is $40 per unit, and sells the product
$90 per unit.
a) Build the economic equilibrium graph.
b) If the plant operates at 90% of its capacity, compare
the annual profit with the generated profit
when it operates at 100%. Assume that the first
90% of the produced capacity is sold at $90
per unit; and the remaining 10% of the production,
$70 per unit.
2.19. The fixed cost per steam line per meter
The pipeline costs $450X + $50 per year. The cost for
the heat loss in the pipe is $4.8/
X1/2 per year. Here, X represents the thickness of the
isolation, in meters, is a continuous variable
of design. (2.4)
a) What is the optimal thickness of insulation?
b) How do you know if the answer to the previous item
minimize the total cost per year?
c) What is the basic exchange analysis that
What is done in this problem?
A farmer estimates that if he harvests his crop
from soy right now, you will obtain 1,000 fanegas,
that can be sold for $3.00 per bushel. Without
embargo, it is estimated that this crop will increase in
1,200 additional fanegas of soy per week
that delays the harvest, although the price will decrease
at a rate of 50 cents per fanega per
week; moreover, it is likely that they will spoil
approximately 200 fanegas weekly for
every week it takes to harvest. When
you should harvest your crop to obtain the most
cash yield, and how much you would receive for your
crop at that moment? (2.4)
2.21. A recent graduate in engineering
he/she received the task of determining the best
production rate for a new type of process
in a mold in a foundry. After experimenting
with many combinations of rates
production per hour and total production cost
for now, he summarized the data he obtained in the
Table I. (See table P2.21). Then, he spoke with
CHAPTER 2 / COST CONCEPTS AND DESIGN OF ECONOMIC MODELS
Tabla I Costo total/hora $1,000 $2,600 $3,200 $3,900 $4,700
100 200 300 400 500
Tabla II Precio de venta/molde $20.00 $17.00 $16.00 $15.00 $14.50
Moldes producidos/hora 100 200 300 400 500
Table P2.21 Table for problem 2.21
the company's marketing specialist, who
gave estimates of the selling price per mold
as a function of the quantity produced (see the
Table II). There are 8,760 hours in a year. (2.4)
a) What production rate would you recommend?
to maximize total profits per year?
b) How sensitive is the rate from the previous section?
to the changes in the cost per hour of production
total?
2.22. The cost of operating a large ship (CO) varies
with the square of its speed (v); specifically,
CO
=knv2, give the length of the journey in
miles, ykes a constant of proportionality.
It is known that at 12 miles/hour the average cost of
operation is $100 per mile. The owner
the ship wants to minimize operational costs,
but it must balance it against the cost of the load
of perishable products (CC), that the customer has
established at $1,500 per hour. At what speed should
to plan to undertake the trip with the purpose
to minimize the total cost (TC), which is the sum of the
operational cost of the ship plus the cost of the
perishable load? (2.4)
2.23. Suppose you are going to take a long trip
to her grandmother's house, who lives in Seattle, 3,000
thousands of miles away. He has decided to make the trip in
his old Ford car, which runs approximately
18 miles per gallon at a speed of 70 miles
for now. Since the grandmother is a
excellent cook and you can stay and eat
at home as much as you want (for free), you wish
moving to Seattle in the most economical way
possible. However, you are concerned about the rate
of gasoline consumption at high speeds.
To balance that high cost, you have
the cost of food, snacks, and accommodation.
What is the optimal average speed at which
should travel to minimize the total cost of
trip,CT? (2.4)
CT
=CG+CFSS, where
CG
=n×pg
×f(CG
gasoline cost
CFSS
=n×pfss
×v−1(Cfss
gasoline cost
snacks and lodging
length of the trip (miles)
$1.26/gallon
pfss: spending money per hour, $2/hour, (motel,
breakfast, snacks, etc., $48 for 24 hours,
average speed of the car (miles/hour)
f = kv, where k is a constant of proportionality
the gasoline consumption rate in
gallons per mile.
2.24. With the information from the table that is presented
Next, solve items a) and b). (2.5)
a) Compare the probable cost of the part in the
Oh the machine B, if it is supposed that
each one will be manufactured with the same specification.
What machine produces the lowest cost?
from the part? Suppose that the interest rate is
despicable.
b) If the cost of labor can be reduced by half
with the use of part-time employees,
Which machine is recommended?
MachineA MachineB
Inversión de capital inicial $35,000 $150,000
Life 10 years 8 years
Valor de mercado (rescate) $3,500 $15,000
Parts that are required
per year 10,000 10,000
Labor cost
per hour $16 $20
Time to manufacture
a part 20 minutes 10 minutes
Maintenance cost
per year $1,000 $3,000
2.25. The following results were obtained after
to analyze the operational effectiveness of a
machine for production with two different speeds:
Exit Time between
pieces for sharpening of the
Speed (hour) tool (hours)
A400 15
B540 10
A non-sharpened tool set costs $1,000.
and can be used 20 times. The cost of each sharpening
It is $25. The time required for the change
and reinstalling the tools takes 1.5 hours,
and the changes are made by a specialist to whom
they pay $15/hour, which includes the time that the
machine stops for its tools to be sharpened.
The general variable costs of the machine
they charge at a rate of $25/hour, which includes
the tool change time. A will be made
fixed-size production run (regardless
of the speed of the machine).(2.5)
a) At what speed should the machine operate?
to minimize the total cost per piece? State
the assumptions I make.
b) What is the basic exchange analysis in
this problem?
2.26. In the tool game for a certain lathe
steel can be used for tools or steel at
carbon. It is