- The Willow Furniture Company produces
tables. The fixed monthly cost of production is $8,000, and the variable
cost per table is $65. The tables sell for $180 a piece.
- For a monthly volume of 300 tables,
determine the total cost, total revenue, and profit.
- Determine the monthly break-even
volume for the Willow Furniture Company.
4. The Evergreen Fertilizer Company
produces fertilizer. The company’s fixed monthly cost is $25,000, and its
variable cost per pound of fertilizer is $0.15. Evergreen sells the
fertilizer for $.-04 per pound. Determine the monthly break-even volume
for the company.
7. Andy Mendoza makes hand crafted dolls,
which he sells at craft fairs. He is considering mass-producing the dolls
to sell in stores. He estimates that the initial investment for plant and
equipment will be $25,000, whereas labor, material, packaging, and shipping will
be about 410 per doll. If the dolls are sold for $30 each, what sales
volume is necessary for Andy to break even?
17. Andy Mendoza in problem 7 is
concerned that the demand for his dolls will not exceed the break-even
point. He believes he can reduce his initial investment by purchasing used
sewing machines and fewer machines. This will reduce his initial
investment from $25,000 to $17,000. However, it will require his employees
to work slowly and perform more operations by hand, thus increasing variable
cost from 410 to $14 per doll. Will these changes reduce the break-even
point?
23. Consider a model in which two
products, x and y, are produced. There are 100 pounds of material and 80
hours of labor available. It requires 2 pounds of material and 4 hours of
labor to produce a unit of x, and 1 pound of material and 5 hours of labor to
produce a unit of y. The profit for x is $30 per unit and the profit for y
is $50 per unit. If we want to know how many units of x and y to produce
to maximize profit, the model is
Maximize Z = 30x + 50y
Subject to
2x + 4y = 100
x + 5y = 80
Determine the solution to this problem
and explain your answer.
- A magazine company had a profit of
$98,000 per year when it had 32,000 subscribers. When it obtained 35,000
subscribers, it had a profit of $117,500. Assuming that the profit P is
linear function of the number of subscribers.
- Find the linear function of P.
- What will the profit be if the company
obtains 50,000 subscribers?
- What is the number of subscribers to
breakeven?
- Musclebound Movers charge $85 plus $40
an hour to move households across town.
- Formulate the linear function of C(t)
for t hours of moving.
- Use the model to determine the cost of
6.5 (6 ½) hours of moving.
- FaxMax bought a multifunction fax for
$750. The value V(t) of the machine depreciates (declines) at at arate
of $25 per month
- Formulate a linear function for the
value V(t) of the machine t months.
- Use the model to determine the value
of the machine after 13 months.
- Consumers demand for a certain product
in a month was 1200 units when the price was $50 per unit. When the
price as $75 per unit, the demand per month was 900 units. Determine the
quantity demanded of this product per month when the price was $90 per
unit.
- Twin Cities Cable TV Services charges
a $35 installation fee and $20 per month for basic service.
- Formulate a linear function for total
C(t) for t months of Cable TV service.
- Use the model to determine the cost of
9 months of service.
9. A boat was purchased for
$44,000. Assuming that the boat depreciates at a rate of $4,200 per year
for the first 8 years, write the value of the boat as a function of time
(measured in years for 0 < t
< 8). What will be the value of the boat after 5
years?
- A manufacturer produces a produces a
product at a cost of $22.80 per unit. The manufacturer has a fixed cost
of $400.00 per day. Each unit retails for $37.00. Let x represent
the number of units produced in a 5-day period.
- Write the total cost C as a function
of x.
- Write the revenue R as a function of
x.
- Write the profit p as a function of
x.
- What will be the profit when 70 units
were produced and sold?
- Determine the number of units required
to breakeven.
Task
Find the equation of a line through the
points (-5, 11) and (8, -7).