THIS IS A SIMPLIFIED VERSION OF THE REQUIREMENTS FOR THIS PROJECT

THIS IS A SIMPLIFIED VERSION OF THE REQUIREMENTS FOR THIS PROJECT

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Widgets

INTRODUCTION
Widgets are in extreme demand because they have become a very valuable tool needed in every household. Etc, etc, etc…
This will be a full time/part time/weekend …
The customer base is Males/Females between the ages of (above the age of/below the age of)…
Advertising will/will not be done…
Other information you want to add here.
NOTE: Be careful using sentences that begin with I will this… . I will that… .

DATA

1,000 people were surveyed and found ___ people are willing to pay ___ for my widget. ___people are willing to pay ___ for my widget.
The supply function was determined by asking suppliers ___, and determining the number of suppliers who are willing…
The equilibrium price was calculated using ____.
The widget’s selling price is $____ , using the equilibrium point.
The cost to make each widget is $______. The raw materials list _____, cost of each raw material $____ by calculating the cost of the raw materials and the cost to manufacture each widget. The fixed cost was determined by averaging_____.

ADD MORE DESCRIPTIVE DETAIL ABOUT YOUR BUSINESS.

SUPPLY AND DEMAND
Supply Function: this describes the relationship between quantity supplied and the selling price.
1. Determine the price of goods related to the product whose supply function you’re attempting to calculate.
2. How many suppliers or producers of the given goods are there?
3. Determine the function on how the given quantities would affect the supply of the product.
NOTE: price of good and number of suppliers are considered to be constant.

EX) One good supplied is the price minus 1/5 the price of related goods + the number of supplies. Q = -1/5 P + P – S

THE FOLLOWING IS AN EXAMPLE OF HOW TO WORK OUT THE EQUATIONS NEEDED FOR THIS PROJECT.
Through careful surveys and data collection, the supply and demand functions were determined using the following process…
PLEASE SEE THE PROJECT OUTLINE FOR NOTES AND COMMENTS OF THE SUPPLY FUNCTION

At $1.40 per widget, the daily supply for widgets is 850 widgets and the daily demand is 850 widgets. When the price falls to $1.20 per widget, the daily supply decreases to 350 widgets, and the daily demand increases to 980 widgets. NOTE: I ASSUMED that the supply and demand equations are linear for this example (PLEASE LET EXCEL CALCULATE THIS FOR YOU USING YOUR DATA).

A-find the supply equation.
B-find the demand equation.
C-find the equilibrium price and quantity.
D-graph the two equations in the same coordinate system and identify the equilibrium point, supply curve, and demand curve

SOLN)
let x1 = 120 cents
let x2 = 140 cents

for the supply equation:
let y1 = 350 widgets
let y2 = 850 widgets
for the demand equation:
let y1 = 980 widgets
let y2 = 850 widgets
the x-axis will represent the price per widget in cents.
The y-axis will represent the number of widgets.

When x = 120, y = 980 for the demand equation, and y = 350 for the supply equation.

SUPPLY EQUATION:

Since this is a linear equation, it will take the slope-intercept form of:

y = mx + b where m is the slope and b is the y-intercept.

The slope is equal to (y2-y1)/(x2-x1) = (850-350)/(140-120) = 500/20 = 25
Substitute any of the 2 points to find the y-intercept.

The equation is y = 25x + b

Now, substitute (140,850) to get 850 = 25*140 + b
Solve for b to get b = 850 – (25*140) = -2650

the supply equation is:

y = 25x – 2650

DEMAND EQUATION:

Since this is a linear equation, it will take the slope-intercept form of:

y = mx + b where m is the slope and b is the y-intercept.

The slope is equal to (y2-y1)/(x2-x1) = (850-980)/(140-120) = -130/20 = -6.5

Now, substitute any of the 2 points to find the y-intercept.

The equation is y = -6.5x + b

Now, substitute (140,850) to get 850 = -6.5*140 + b

Solve for b to get b = 850 – (-6.5*140) = 1760

The demand equation is:

y = -6.5x + 1760

you have two linear equations.
y = 25x – 2650 (supply equation)
y = -6.5x + 1760 (demand equation)
Use Excel to graph these equations:
supply equation Demandequation
y = 25x – 2650 y = -6.5x + 1760

x y x y
110 100 110 1045
120 350 120 980
130 600 130 915
140 850 140 850
150 1100 150 785
160 1350 160 720
170 1600 170 655
180 1850 180 590
190 2100 190 525
200 2350 200 460

Graph these equations to get:

The demand equation is sloping downwards. As the price increases, the demand goes down.Thesupply equation is sloping upwards. As the price increases, the supply goes up.

Theequilibrium point is when x = 140 cents which is equivalent to $1.40 per widget.
NOTE: The equilibrium point is when the demand equals the supply.
Calculate supply and demand with a slight increase and decrease in price. And explain what happens.

COST AND REVENUE

Cost and Revenue

Each widget will sell for $1.40.

The revenue function is: R(x) = 1.40x

The cost of the raw materials to produce each widget is $0.25

Utilities, Manpower, Insurance, and Maintenance was averaged over a period of 3 months to determine the fixed cost for each day is $10

The cost function is: C(x) = 0.25x + 10
Cost Revenue
C(x) = 0.25x + 10 R(x) = 1.4x
x C(x) x R(x)
1 10.25 1 1.4
2 10.5 2 2.8
3 10.75 3 4.2
4 11 4 5.6
5 11.25 5 7
6 11.5 6 8.4
7 11.75 7 9.8
8 12 8 11.2
9 12.25 9 12.6
10 12.5 10 14

Break Even Point

C(x) = R(x)
0.25x + 10 = 1.40x
x = 8.7
9 widgets need to be sold each day in order to break even.
PROFIT
Profit Function:
Determine what will happen to your profit when the price of your product is increased and decreased from your equilibrium point.
P(x) = 1.40x – 0.25x + 10 = 1.15x + 10

PREDICTIONS

If the price were to be increased to $1.50 ($0.10 above the equilibrium point). And decreased to $1.30 ($0.10 below the equilibrium point).
(785 people will buy at $1.50 and 915 people will buy at $1.30)

NOTE: you can choose any value you want above and below the equilibrium point.
What happens to your supply, cost, revenue, and profit functions?
NOTE: you can determine the number of widgets you will sell by looking at the supply and demand graphs. If the price is increased, less people will buy. Evaluate the cost/revenue/profit calculations based on the number of people (x) buying widgets.

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