# Quantitative Methods

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).

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#### Solution Preview

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.

FC=$8000

VC=$65/table

SP=$180

Q=300 tables

Profit = Revenue - Variable cost - Fixed Cost

Revenue=SP*Q = $180*300 = $54,000

Total cost= Total fixed cost + Total variable cost = $8000+65*300 = $27,500

Total cost= $27,500

Profit=$54000-27500 = $26,500

BEV=FC/SP-VC = 8000/(180-65) = 69.56 Tables

Monthly Break Even Volume=70 tables

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 $.40 per pound. Determine the monthly break-even volume for the company.

FC=$25,000

VC=$0.15/pound

SP=$0.40

BEV=FC/SP-VC = 25000/(0.40-0.15) = 100,000 Pounds

Monthly Break Even Volume for the company =100,000 Pounds

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 $10 per doll. If the dolls are sold for $30 each, what sales volume is necessary for Andy to break even?

FC=$25,000

VC=$10

SP=$30

BEV= BEV=FC/SP-VC = 25000/(30-10)=1250 Dolls

Break Even Volume for Andy =1250 Dolls

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 ...

#### Solution Summary

This posting provides solution to several problems on quantitative methods including linear function, breakeven, etc