Question

Homer’s Donuts is a small-business startup looking to open its first franchise location in Smallville. Your ownership team completed its business and marketing SWOT (“strengths – weaknesses – opportunities – threats”) analyses and believes there’s a real chance for Homer’s Donuts to be a successful business!

The SWOT marketing analysis included a survey of potential customers in and around the Smallville metropolitan area. The survey asked people what pastries they would most likely buy when they stop for coffee on the way to wherever they were going. 2500 people responded to the survey, and the results are as follows:

1765 respondents said they would buy glazed donuts

1738 respondents said they would buy creme-filled frosted donuts

347 respondents said they would buy neither glazed nor creme-filled frosted donuts

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Task 1: Interpreting the Marketing Survey: Counting

For the survey results above:

Create either a Venn diagram or a contingency table depicting the results of the survey.

Determine how many of the survey respondents would buy either a glazed donut or a creme-filled frosted donut?

Determine how many of the survey respondents would buy a glazed donut and a creme-filled frosted donut?

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From your SWOT analyses, your team decides the best way to go is to offer assorted donuts, sold individually or by the dozen. Now your team has to come up with a daily operation cost/revenue analysis to see if it’s actually worth going into business. Here’s what the team knows so far:

Before making any donuts, there is a $784 fixed cost each day (which covers the building and its equipment, as well as labor costs for 2 shifts of 4 employees each). That means the cost to produce 0 dozen assorted donuts per day is $784. The cost to produce 50 dozen assorted donuts per day is $809; the cost to produce 90 dozen assorted donuts per day is $829; and the cost to produce 120 dozen assorted donuts per day is $844. The relationship between dozens of donuts produced per day and cost per day is linear.

To undercut the competition, your team recommends setting the price per dozen assorted donuts so that Homer’s gets $255 total (gross) income for 30 dozen assorted donuts sold per day, and $935 total (gross) income for 110 dozen assorted donuts sold per day. The relationship between dozen donuts sold per day and total (gross) income per day is linear.

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Answer 1

Task 1

Note: Given figures are in bold font. Others are derived.

	Buy creme-filled frosted donut	Not buy creme-filled frosted donut	Total
Buy glazed donuts	1350 [1765 – 347]	415 [762 – 347]	1765
Not buy glazed donuts	388 [1738 – 1350]*	347	735 [2500 - 1765]
Total	1738	762 [2500 - 1738]	2500

[Note: *Check that 388 is also equal to (735 - 347)

ANSWER 1

Number of respondents who would buy either a glazed donut or a creme-filled frosted donut

= Number of respondents who would buy only glazed donut + Number of respondents who would buy only creme-filled frosted donut + Number of respondents who would buy both

= 415 + 388 + 1350

= 2153 ANSWER 2

Number of respondents who would buy both = 1350 ANSWER 3

[Going beyond,

Answer 2 can also be obtained from(Total – Neither) = 2500 – 347 = 2153.

Yet another way is: (glazed donut + creme-filled frosted donut – both) = 1765 + 1738 – 1350 = 2153]

DONE

Second Part: Feasibility Analysis

Given ‘there is a $784 fixed cost each day (which covers the building and its equipment, as well as labor costs for 2 shifts of 4 employees each). That means the cost to produce 0 dozen assorted donuts per day is $784. The cost to produce 50 dozen assorted donuts per day is $809; the cost to produce 90 dozen assorted donuts per day is $829; and the cost to produce 120 dozen assorted donuts per day is $844. The relationship between dozens of donuts produced per day and cost per day is linear., Let cost of producing n dozens of assorted donuts be: C = a + nb. Then, we have:

a = 784, b = 0.5 and hence C = 784 + 0.5n

Similarly, given, ‘price per dozen assorted donuts so that Homer’s gets $255 total (gross) income for 30 dozen assorted donuts sold per day, and $935 total (gross) income for 110 dozen assorted donuts sold per day. The relationship between dozen donuts sold per day and total (gross) income per day is linear.’ Let gross income of selling n dozens of assorted donuts be: R = A + nB. Then, we have:

A = 0, B = 8.5 and hence R = 8.5n

Equating C and R, thebreak-even n = 98.

Thus, so far as the company can produce and sell 98 dozen assorted donuts, the project is worthwhile. ANSWER