20 question business math quiz. Must show work for all questions, expect multiple choice. All question have the required information to solve

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Question 1

Elderwood Tree Farm grows and sells landscaping trees. The fixed monthly cost of land and

equipment is $6,450 and the variable cost per tree is $36. The trees sell for $75 apiece. What is

the break-even volume for the company? What are the total cost, revenue, and profit for selling

182 trees?

Question 2

A model in management science is:

Select one:

a. a previously unknown problem.

b. a symbol representing a numeric value.

c. a graph or chart.

d. an abstract representation of an existing problem situation.

e. a small-scale recreation of a factory or warehouse.

Question 3

Darcy Fashions produces hand-stitched dusters and riding coats. Their fixed costs are $2,300 per

month. The variable cost per coat in materials and labor is $65. They sell the coats for $120 each.

Find the break-even point for how many coats they must sell in a week. How much profit do they

make in a month if they sell 40 coats per week? A more skilled workforce to do the stitching

would increase the variable cost to $95 per coat, but would increase quality and allow the coats

to sell for $210 each. What is the new break-even point for the week? How much monthly profit

would they now make selling 40 coats per week? How few coats could they sell per week and

still match the profit from the original situation?

Question 4

Gregory’s company has ordered a large supply of paint, but the manufacturer says there is a

possibility that the batch they received was defective. However, the company has no choice but

to start filling orders, and they are trying to decide where they can safely use the paint. They

estimate their profits based on expected rates of return for different products if the paint

fails. What does the maximax criterion and the maximin criterion support?

Product

Table/chairs

Cabinets

Paint is not defective

$16,600

$35,450

Paint is defective

$350

-$4,750

Fixtures

Dressers

$18,450

$22,000

-$750

-$2,050

Question 5

Should OTELO LLC. put in a project proposal for the Baker Street development? What kind of

proposal should they put in? Evaluate the payoff table below using the maximax, maximin, and

minimax regret criteria.

Decision

Win contract

Business proposal $1,650,000

Mixed proposal

$1,455,000

Residential proposal$1,340,000

No proposal

$0

Lose contract

-$18,500

-$16,400

-$2,000

$0

Question 6

Delicatessen Catering Co. provides catering services for weddings, reunions, business functions,

and a variety of other social events. Delicatessen is thinking of hiring more staff to keep up with

rising demand. This would require purchasing more equipment and vehicles to ensure these staff

can do their jobs. Determine what choice they should make using the Hurwicz (α = 0.7 and α =

0.4) and equal likelihood criteria. What are the expected values?

Decision

Increased demand

Decreased demand

Hire staff

Do not hire

$25,040

$5,650

-$18,950

$4,970

Question 7

Home Furnishings and Decorations Inc. can revamp the loading area of their warehouse to

improve the efficiency of loading trucks. They have two possible proposals for the work, one

that modernizes their current setup and one that is a new layout, which would be a sweeping

change in workflow but promises a huge gain in efficiency for high volumes of traffic. The new

layout, however, is a lot more expensive to build. Use the payoff table to determine the expected

profit or loss for each purchase, and determine the optimal purchase.

Plan

Gain clients (0.4)

No change (0.4)

Lose clients (0.2)

New loading layout $32,400

Modernized layout $12,290

No change

$9,400

$5,250

$10,050

$0

-$45,450

-$10,800

-$2,600

Question 8

Boutique Guitars and Gear carries several types of strings. For one type, each package of strings

costs the store $3.50 to purchase, and the store can sell them for $6.50 a piece. He estimates that

not having the strings in stock if someone wants them costs him about $0.50 in business

goodwill. However, after 6 months the strings start to age and he has to drop the prices to $2.50

per pack to get them to sell. He estimates demand for the strings in the next 6 months using the

table below. Generate a payoff table, and compute the expected value for each alternative. How

many packs of strings should the guitar shop purchase?

Demand

10

11

12

13

14

Probability

0.10

0.15

0.35

0.25

0.15

Question 9

John Smith Framing has noticed that a lot of customers would like to be able to print

photographs to frame. But since the store does not have an art printer, customers have to get their

photos printed elsewhere. The manager, John, is deciding between three possible printers,

estimating their profitability based on what sorts of materials they could print and what the

expected demand for those services is. Using the information below, create a decision tree for

John Smith Framing and compute the expected value for each printer. Which printer should the

framing store purchase?

Location

Increasing demand (0.22) Steady (0.68) Falling (0.1)

Magnaprint

$10,700

430f

VistaVox md82$8,650

ArtStock Pro 5 $15,450

Question 10

$3,540

$1,200

$5,480

$2,300

$3,410

-$2,710

Delaware Coffee Roasters, LLC. is considering moving its coffee roasting operation from the back of the

store to some neighboring warehouse space. The company has to decide how much space to rent and

how to handle sales and distribution. They make a payoff table, shown below. Determine the expected

value for each alternative using the given probabilities.

Acquire

4,000 sq. ft, new trucks

4,000 sq. ft, keep truck

2,000 sq. ft, new trucks

2,000 sq. ft, keep truck

Stable economy (0.65)

$105,000

$84,200

$74,350

$56,750

Slowing economy (0.35)

-$65,450

-$25,300

-$38,900

-$15,250

Question 11

Construct a Gantt chart for the following set of activities. Indicate the total project completion

time and the slack for each activity. Submit a plain text version of your Gantt chart by using

dashes to represent activity lengths (e.g., —- for 4 months).

Activity

1

2

3

4

5

6

7

8

Predecessor

1

1

2,3

4,5

6

7

Time (months)

6

8

4

3

7

1

5

4

Question 12

Using the CPM/PERT network below, with times measured in weeks, find the critical path and

the slack times for each step. What is the project completion time? For each node, the step

number is written on top and the time written on the bottom.

Question 13

Using the activity table below, construct a CPM/PERT network noting the activity numbers and

durations. Identify the critical path through the network, determine the project completion time,

and determine the earliest and latest start dates for each node. Create your network in Microsoft

Word and submit it to your instructor.

Activity

1

2

3

4

5

6

7

Predecessor

1

1,2

3

3

4,5,6

Time (days)

2

8

3

6

3

5

10

Question 14

The activity table below corresponds to a project with critical path 1 → 4 → 5 → 6 → 8. Find the mean

lengths and variances of each task on the critical path.

Activity

1

2

3

4

5

6

7

a

6

4

3

4

1

11

8

Times (days)

m

10

9

7

5

3

13

10

b

12

14

20

8

7

16

12

8

3

6

8

Question 15

Use the activity table below. Find the project completion time. What is the combined cost of tasks on

the critical path only?

Activity

1

2

3

4

5

Predecessor

1

2

3, 4

Time: (weeks)

6

2

4

5

6

Cost: ($)

6,400

2,500

5,500

6,400

6,600

Question 16

Solve the linear programming problem.

Minimize Z = 42x + 10y

subject to

2x + 2y ≥ 80

x + 6y ≥ 200

x, y ≥ 0

Question 17

Solve the linear programming problem by graphing. Graph the feasible region, list the extreme

points and identify the maximum value of Z. You do not have to submit your graph, but please

list the equations of the lines that form the feasible region.

Minimize Z = 4x + 6y

subject to

2x + 4y ≥ 20

3x + 2y ≤ 24

x, y ≥ 0

Question 18

Tamlin Architectural is building a new, green apartment building downtown. In order to maintain the

building’s eco-friendly status, the carbon footprint of the building’s heating systems needs to be kept as

low as possible. The architectural firm has two kinds of heating units available. A solar heater costs

$13,000, provides 400 W of heat, and has a carbon footprint of 0.6. A heat pump costs $4,500, provides

800 W of heat, and has a carbon footprint of 4.2. The architects need at least 12,000 W of heat for the

building, and cannot spend more than $261,000 on the heating system. How many of each type of

heater should Tamlin Architectural use in order to meet the criteria while minimizing the carbon

footprint? Formulate a linear programming model for this situation. Solve this model using graphical

analysis. Display your graph and the solution parameters. Create your graph using Microsoft Word or

Excel and submit it to your instructor.

Question 19

Trinity Bus Lines wants to maximize the number of passengers it can carry from Far Point to Newtown.

Bus A can carry 60 passengers and costs $2,700 per month to run. Bus B can carry 48 passengers and

costs $1,800 per month to run. The bus line has a maximum of 12 drivers, and can spend no more than

$24,300 per month on running the buses. What is the maximum number of passengers they can carry,

and which buses should they purchase? Formulate a linear programming model to solve this problem.

List the extreme points and determine the solution graphically. You do not need to submit your graph.

Question 20

Jericho Agricultural Supply is mixing a fertilizer to sell to farmers. The agricultural supplier creates two

fertilizer blends out of pure ingredients. Blend A uses 10 lbs of nitrogen and 10 lbs of phosphate in each

20 lb bag. Blend B uses 16 lbs of phosphate and 4 lbs of nitrogen in each 20 lb bag. A bag of Blend A sells

for $16, while a bag of Blend B sells for $18. The supplier has 200 lbs of phosphate and 240 lbs of

nitrogen to work with. How many bags of each kind of fertilizer should the agricultural supplier mix to

generate the maximum gross income? Formulate a linear programming model and solve it graphically.

Display your graph and calculate the maximum gross income. Create your graph using Microsoft Word

or Excel and submit it to your instructor.

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