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Spring 2010 George Banis Nick Hoover Michelle Marini Laura Mueller-Soppart Cher Rui

[FROM BABY TO BUSINESS] A T-SHIRT SALES CAMPAIGN Course: MATH1111. Northeastern University, Spring 2010. Instructor: Stanislav Dubrovskiy.


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Contents Flyer Design .................................................................................................................................... 3 Part A .............................................................................................................................................. 4 Design and Planning; Estimate of Costs ..................................................................................... 4 A1: Target Market: .................................................................................................................. 4 A2: Design the Shirt: ............................................................................................................... 4 A3: Marketing Plan: ................................................................................................................ 5 A4: Reachable Target Market: ................................................................................................ 5 A5: Unit Cost:.......................................................................................................................... 6 A6: Fixed Costs: ...................................................................................................................... 6 A7: Polling Plan: ..................................................................................................................... 6 Part B .............................................................................................................................................. 7 Poll Your Market and Tabulate the Results ................................................................................ 7 B2-B4: Responses: .................................................................................................................. 7 B5: ........................................................................................................................................... 8 B6: Create a Scatter Plot:......................................................................................................... 8 Part C .............................................................................................................................................. 9 Model the Demand, Revenue, and Profit Functions ................................................................... 9 C1: Model the Demand Function D(x): ................................................................................... 9 C2: Revenue Function, R(x): ................................................................................................. 10 C3: Cost Function, C(x): ....................................................................................................... 11 C4: Profit Function, P(x): ...................................................................................................... 11 Part D ............................................................................................................................................ 12 Optimization .............................................................................................................................. 12 D1 Maximize Revenue and Profit ......................................................................................... 12 D2 .......................................................................................................................................... 13 D3 .......................................................................................................................................... 13 D4 .......................................................................................................................................... 13 D5 .......................................................................................................................................... 13 D6 .......................................................................................................................................... 14 D7 .......................................................................................................................................... 14 D8 .......................................................................................................................................... 15

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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Flyer Design

From Baby To Business: A tt-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Mueller Soppart, Cher Rui Northeastern University, Spring 2010


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Part A Design and Planning; Estimate of Costs A1: Target Market

The following business proposal involves the creation, production, and distribution of t-shirts throughout the Northeastern College of Business community. The College of Business has approximately 3,001 students in total; 2,171 in classes, living on campus, and 830 working on co-op, either living on campus or not (phone call to Mary Boudreau, Assistant to Director CBA Co-op, 617-373-4225). Since the students on co-op are likely working during the times we've specified to sell our t-shirt, our target audience is only 2,171 students.

A2: Design the Shirt

The appeal of the proposed t-shirt design is its uniqueness. Majority of past t-shirt designs targeted towards business majors have encompassed the stereotype of the student: serious, bland, and to the point. The following proposition plans to give students a young, hip option. The t-shirt will be one sided. It will have one background color, white. There will be one image in black, the silhouette of the "evolution of the business student". Underneath said image will be a tag line in red that reads: "Evolution: From Baby to Business"

Concepts: One Sided Background Color (White) 2 colors (Red Text, Black Image) Price per T-shirt (not including ad's) = $3.90 From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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A3: Marketing Plan

These t-shirts will be available for sale during Undergraduate Activities Period. Mondays: 12pm1pm; Wednesdays 12pm-1pm; Thursday 3pm-4pm, for the remaining duration of the Spring 2010 semester. A table will be set during this time period outside of Dodge Hall in Krenztman Quad. A great number of business classes are situated in the buildings surrounding this area of campus. The activities period is a time when no formal classes are in session so the potential market is increased because students will be leaving class, but will not be hurried to their next, and therefore will have a greater chance of having a spare moment to purchase a t-shirt.

A4: Reachable Target Market

Advertising would stem from flyers in these buildings. Because promotions will be visible all week through flyers, and three days a week there will be a physical sales stand, the probability that all business students pass through Krenztman Quad at least once during this time frame is near certain. In addition, the business school list server used by administrators will be utilized to promote the t-shirts through professors Peggy O' Kelly and Andre Switala who will send out a mass email to their students. This email list server reaches all 3,001 students. Therefore it is predicted that our reachable market is 2,171 students * 90% = 1,954 students.

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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A5: Unit Cost

Since the reachable target market is 1,954 students, half of this market is 977 students. Therefore for now we will order the "over 501-above" range. We have a one sided, two color design. The white shirt, $3.75/t-shirt, has an additional charge for a two color pattern of $0.15/t-shirt, totaling the unit cost to $3.90/t-shirt.

A6: Fixed Costs

The fixed costs will include the price of a table and flyer production. The fixed cost of purchasing a table to display our shirts is $60.00 from Office Max. The fixed cost of a color copy at Gnomon copies is $0.20. We will print 100 flyers. The fixed cost of the flyer production is $20.00. The total fixed costs is $80.00 for 15 weeks of selling t-shirts.

Total cost of production is $3.90/t-shirt * 1,350 t-shirt is $5,262. Including the fixed costs, the total expenditure is equal to $5,265 + $80.00 which is $5,345.00.

A7: Polling Plan

The plan of execution for the polling is to have professors Peggy O' Kelly and Andre Switala not only send out flyers, but also to send out a poll asking the students to fill out including the price they'd be willing to pay for the shirt, some information about their graduation year, concentration, and when they pass through Krentzman Quad. With the survey landing in all of our target markets email, the response will be much greater than the 50 required. The use of the list server has already been outlined as having a 90% outreach capability.

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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Part B Poll Your Market and Tabulate the Results B2-B4

Price ($)

Responses

Cumulative Responses

Demand

15

3

3

95

14

0

3

95

13

2

5

158

12

2

7

221

11

3

10

315

10

9

19

599

9

5

24

756

8

10

34

1,072

7

6

40

1,261

6

5

45

1,418

5

9

54

1,702

4

1

55

1,733

3

2

57

1,796

2

0

57

1,796

1

0

57

1,796

0

5

62

1,954

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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B5

We decided to do the polling ng online. In order to be more effective we sent the poll to students taking the classes ACCT1201 and ECON1115 (professors P. O'Kelly, A. Switala). We also asked friends who are business majors reply to the online poll.

The poll consisted of 5 fields: 1. Dollars willing to spend on the t-shirt, shirt, 2. What time students are most likely to pass through Krentzman Quad, 3. Their name (optional), 4. Their year of graduation (optional), and 5. Their concentration (optional). Students replied though dates 2/8/10 to 2/16/10.

Reactions were not measured because of the nature of the online poll. Poll participants had no access to previous participants' responses.

B6: Create a Scatter Plot

From Baby To Business: A tt-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Mueller Soppart, Cher Rui Northeastern University, Spring 2010


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Part C Model the Demand, Revenue, and Profit Functions C1: Model the Demand Function D(x):

Logistic

y=c/(1+ae^(-bx))

a=0.115543762

b=-.5350966398

c=1898.791102

D(x)= 1898.7911023582/(1+0.0115543762496e^(0.53509663955086x)

D(x) =

ଵ଼ଽ଼.଻ଽଵଵ଴ଶଷହ଼ଶ ଵା଴.଴ଵଵହହସଷ଻଺ଶସଽ଺ୣబ.ఱయఱబవలలయవఱఱబఴల౮

t-shirts

The logistic model is the best fit for the curve not only because it fits the points of the data and comforms to the concavity, but also because it accurately depicts the end-point behavior. Since our data shows that as the price of the t-shirt approaches $15 dollars the demand approaches 0, we know that any price beyond $15 would lower the demand but never cross 0 (as negative demand isn't feasible). Furthermore, on the other end of the curve, as the price approaches $0 the

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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demand increases to nearly 2,000. However, the lowest price we can technically sell the shirt for can be no less than $0 dollars and therefore the demand would not continue to increase.

The model does serve as a reasonable predictor for future demand based on the prices. When the price of the t-shirt is $20, D(20)=3.96, which serves to show that the demand will continue to decrease as the price of the t-shirt increases.

C2: Revenue Function, R(x):

R(x) = (selling price)(number sold) = (selling price)(demand) =

x(1898.7911023582/(1+0.0115543762496e^(0.53509663955086x))) dollars

R(x) = x

ଵ଼ଽ଼.଻ଽଵଵ଴ଶଷହ଼ଶ ଵା଴.଴ଵଵହହସଷ଻଺ଶସଽ଺ୣబ.ఱయఱబవలలయవఱఱబఴల౮

dollars

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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C3: Cost Function, C(x):

C(x)=(variable cost)+(fixed costs) = (unit cost*number sold)+(fixed costs) =

(unit cost*D(x))+(fixed cost) =

3.9(1898.7911023582/(1+0.0115543762496e^(0.53509663955086x)))+80 dollars

C(x) = 3.9

ଵ଼ଽ଼.଻ଽଵଵ଴ଶଷହ଼ଶ ଵା଴.଴ଵଵହହସଷ଻଺ଶସଽ଺ୣబ.ఱయఱబవలలయవఱఱబఴల౮

+ 80 dollars

C4: Profit Function, P(x):

P(x) = R(x)-C(x) =

[x(1898.7911023582)-3.9(1898.7911023582)]/[(1+0.0115543762496e^(0.53509663955086x)80] (dollars)

P(x) = (x − 3.9)

ଵ଼ଽ଼.଻ଽଵଵ଴ଶଷହ଼ଶ ଵା଴.଴ଵଵହହସଷ଻଺ଶସଽ଺ୣబ.ఱయఱబవలలయవఱఱబఴల౮

− 80 dollars

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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Part D Optimization D1: Maximize Revenue and Profit

Results when maximizing revenue:

The price ($) that maximizes revenue is x = 6.6002502

Math Results

Price

Demand

Revenue

Cost

Profit

$ 6.60

1361

$ 8,984.00

$ 5,388.72

$ 3,595.27

$ 6.50

1382

$ 8,980.35

$ 5,468.21

$ 3,512.83

Business Results

Results when maximizing profit:

The price ($) that maximizes profit is x = 8.0027424

Math Results

Price

Demand

Revenue

Cost

Profit

$ 8.00

1035

$ 8,276.58

$ 4,114.83

$ 4,161.75

$ 8.00

1035

$ 8,276.58

$ 4,114.83

$ 4,161.75

Business Results

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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D2

Revenue reaches its maximum when the price is relatively low since more people want to buy the product and thus it sells more units; the lower the price, the higher the demand. However, if the price is low then the cost is a larger portion of the revenue than if the price was higher. The producer has to transfer some of the costs of production to the consumer in order to gain more profit. This is why we expect the price which maximizes profit to be relatively higher than the price that maximizes revenue.

D3

The (math result) price that maximizes revenue is $ 6.60.

P'(6.60) = 804.43 $/$ (dollars of profit / dollars of price)

In order to calculate the marginal profit, we used nDeriv(P(X), X, X) when x=6.60.

D4

We would use the price that maximizes profit and sell the t-shirts for the $8.00 price because this way we will have the highest possible monetary gain in the short-run.

D5 The demand of the t-shirt when the price is set to $8.00 is D(8) = 1035 t-shirts. In part A we we found our target market to be 1,954 and we assumed half would buy the t-shirt in order to estimate the t-shirt cost, this estimate is 977 students. For more than 501 t-shirt the

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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manufacturing cost remains constant at $3.90 per t-shirt, thus we have no change in the cost to manufacture the t-shirts.

D6

Since we bought 977 t-shirts, the variable cost is $3.90/shirt and the fixed cost (for buying a table) is $80. This makes our new cost function be:

C(X)= 3.9(977)+80= 3890.30

In other words, without having polled the target market and instead choosing to purchase 977 tshirts, the cost would be set at $3,890.30.

P(x) = R(x) - C(x)

P(x)= x(1898.7911023582/(1+0.0115543762496e^(0.53509663955086x))) – 3890.3 dollars

D7

If the new demand function is double the old, then:

Dnew(x) = 2 D(x) => Dnew'(x) = [2 D(x)]' => Dnew'(x) = 2 D'(x)

To find a max we need to find the x which make Dnew'(x) = 0

Dnew'(x) = 0 => 2 D'(x) = 0 => D'(x) = 0

If we see back at part D1, where we have calculated D'(x) = 0

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


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we find out that the answer is x = $6.60

We have confirmed point (6.60, 8,984) is a local maximum by plotting the new demand function.

Thus when the price of the t-shirt is $ 6.60, the revenue reaches its maximum, which is $8,984.00

D8

If we add $ 125.00 to our fixed costs then the new profit function is:

Pnew(x) = Rnew(x) - Cnew(x) = R(x) - [ C(x) + 125 ] = [ R(x) - C(x) ] - 125 = P(x) – 125

To find the maximum profit we need to find the x for which Pnew'(x) = 0

Pnew'(x)=0 => [P(x) - 125]' = 0 => P'(x) = 0 If we see back at part D1, where we have calculated P'(x) = 0 we find out that the answer is x = $8.00

\ We have confirmed point (8, 4,161.75) is a local maximum by plotting the new profit function. Thus when the price of the t-shirt is $ 8.00, the profit reaches its maximum, which is $4,161.75

From Baby To Business: A t-shirt sales campaign by: George Banis, Nick Hoover, Michelle Marini, Laura Mueller-Soppart, Cher Rui Northeastern University, Spring 2010


From Baby To Business