This document analyzes the costs, revenue, and profit of a new portable wireless speaker produced by Vignette. It identifies that maximum weekly profit of $7,491.03 can be achieved by producing and selling 715 speakers. The optimal price was determined to be $21.30, as higher prices would decrease demand and revenue. The analysis provides Vignette with valuable information to price the speaker in a way that maximizes ongoing profitability and benefits the company and its stakeholders.

1. Vignette’s Portable Wireless Speaker: Analysis of Cost, Revenue and Profit
The purpose of this analysis is to evaluate and understand the cost, revenue and profit of
Vignette’s s new portable wireless speakers. The company has just created their new speakers
and wants to ensure they have correctly priced the product to ensure maximum profit. It is
beneficial for both the organization and its stockholders to understand the varying prices and
profit factors. It is hoped that this report will yield valuable information to aid in the success of
Vignette and their new product.
For this analysis, the total cost function, C(x) (see equation 1 in the appendix) was
provided from previous data the company collected. Additionally, the equation for quantity of
speakers demanded (x) based upon given prices was available (equation 2). From such equation,
the revenue function R(x) was yielded (equation 3). Using both the total cost function and
revenue function, the profit function was found (equation 4). A visual representation of the data
is found on figure 1 (the grey curve). The total cost function (the blue line in figure 1) illustrates
the cost increasing at an interval of [0, ) with a concave upward shape. This means, that the
total cost for manufacturing the portable wireless speakers increases at an increasing rate as
additional units are produced. The revenue function is a quadratic (equation 3) which increases
from units 0 to 1,000 which then decreases from 1,000 to 1,500 units at the interval [0, ) with a
downward concavity (orange curve in figure 1).
Marginal revenue was found using differential calculus methods (equation 5). The
analysis resulted in the identification of the global maximum revenue to be $25,205.00 with
production of 1,184 units per week. After reaching the 1,184 units, revenue starts decreasing as
costs for excessive production and other factors such as equipment maintenance and upgrades
occur. The elasticity of demand equation (equation 7) was derived from the data Vignette
collected. It was used to determine that $21.30 is the price at which the demand is unitary. This
means that $21.30 is the highest price the company can set for the wireless speakers without
seeing a decrease in demand and a decrease in revenue.
With the main concern of the company and its stakeholders being profit from the portable
wireless speakers, analysis of the marginal profit is required. The marginal profit function
(equation 6) displays weekly profit of $7,491.03 with a maximum quantity of 715 units. Figure 2
shows the profit and marginal profit functions where the primary vertical axis (on the left) and
the secondary vertical axis (on the right). The primary axis has a range of -8,000 to 10,000 while
the secondary vertical axis has a range of -40 to 40. The marginal profit function shows the
company anticipates to receive a profit of $32.83 for the first wireless portable speaker sold.
Beyond each unit sold after the first there is decreasing profit per unit at a linear rate. For
example, the marginal profit for the 301th unit sold is $19.08. There is decreasing marginal profit
until the production of the 715th unit. Upon the production of the 715th unit there is no profit
made, so the company is operating at a loss for the wireless speakers which could be result of
extensive operational expense. For example, upon producing the 801st unit there is a loss of
$3.97.
The purpose of this case was to analyze the the cost, revenue and profit related to the
portable wireless speaker. The outcome concluded the maximum profit is achieved with the sale
of 715th speakers per week which results in a maximum revenue of $7,491.03. There is hope that
the Vignette may use this information to to better understand and implement the optimal price
for the portable wireless speakers that will have an ongoing favorable impact on the company
and its bottom line.

2. APPENDIX:
Supporting equations, Tables and Graphs
C(x) = .005x2 + 9.72x + 4260 (1)
p = -.018x + 42.60 (2)
R(x) = -.018x2 + 42.60 (3)
P(x) = -.023x2 + 32.88x – 4260 (4)
R’(x) = -.036x + 42.60 (5)
P’(x) = -.046x + 32.88 (6)
e(p) = p/(42.6-p) (7)

3. Figure 1: Graph of Total Cost, Revenue and Profit Functions for Portable Speakers

4. Figure 2: Graph of Profit and Marginal Profit Functions