calculus.application in business supply demand break even anal graph
DESCRIPTION
supply and demand functionTRANSCRIPT
Linear Demand curve with Negative Slope
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5 10 15 20 25 30
y-intercept
x-intercept
Linear Demand curve with zero slope
Linear Demand curve with undefined slope
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-5 5 10 15 20 25
x=a
(a,0)
Linear Supply curves with positive slope
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5 10 15 20 25 30
SS
S
Linear Supply curve with zero slope
S
Linear Supply curve with undefined slope
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8
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4
2
-2
-5 5 10 15 20 25
x=a
(a,0)
S
Given the following linear equations, each
representing either a SUPPLY or DEMAND curve:
X-6y+9= 0 and 2x+3y-12= 0
Where, x represents the QUANTITY in hundreds of units
y represents the UNIT PRICE in tens of pesos
a) Identify which represents a demand
curve and which represents a supply
curve.
Given the following linear equations, each
representing either a SUPPLY or DEMAND curve:
X-6y+9= 0 and 2x+3y-12= 0
Where, x represents the QUANTITY in hundreds of units
y represents the UNIT PRICE in tens of pesos
b) Determine the market equilibrium point
algebraically.
c) Sketch the curves on the same coordinate
axes and indicate the market equilibrium
point.
The BREAK-EVEN CHART is a graphical
representation showing the relationship
among the TOTAL REVENUE (R), TOTAL COST
(Yc), and FIXED COST (FC) equations.
SOME IMPORTANT FEATURES IN THE BREAK-EVEN
ANALYSIS ARE THE FOLLOWING:
1. The FIXED COST LINE (FC) is parallel to the x-axis (hence, the
slope is zero) with y-intercept equal to the FIXED COST. Fixed costs
include all indirect costs and these exist regardless of whether
production takes place or not. These include overhead expenses
such as RENT, SALARIES OF PERSONNEL or ADMINISTRATIVE
SALARIES, PROPERTY TAXES, UTILITIES, INSURANCE, INTEREST ON
BORROWED CAPITAL, MAINTENANCE and DEPRECIATION OF OFFICE
EQUIPTMENT and MACHINERY. The fixed cost equation is Y= FC.
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FC
The TOTAL COST LINE slopes upward to the
right ( slope is positive) with its y-intercept
equal to the fixed cost. The total cost for
the production of a particular commodity in
a specified period of time has two distinct
components: FIXED COST and VARIABLE COST.
VARIABLE COSTS are directly proportional to the level of
production, that is, variable costs increase as quantity of
production increases. These include expenses for WAGES
or direct labor, raw materials and all others directly
related to the production or manufacturing process.
The TOTAL COST LINE equation is given by
Yc = total variable costs + fixed costs
OR
Yc = (variable cost per unit) X + fixed costs
where X pertains to the quantity of
production and Yc, to the toal cost. The
graph shows the relationship among FIXED
COST and VARIABLE COST and TOTAL COST.
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TOTAL COSTfixed cost
variable cost
Yc
FC
The TOTAL REVENUE LINE has a positive slope
and always passes through the origin (0,0)
since NO OUTPUT or NO SALES means NO
INCOME or NO REVENUE. The total revenue
equation can be stated as:
R= (selling price per unit) X
where X is the quantity of commodity
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R
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R
Yc
FC
Based from the figure, there is a point A where the REVENUE LINE intersects the FIXED COST LINE or where R=FC. Thus, solving the REVENUE and FIXED COST equations simultaneously will yield the value of X where revenue is just enough to recover fixed costs.
There is also a point in the graph where R=Yc. Thus, solving the revenue and total cost equations simultaneously will yield the value of x necessary for the producer to earn just enough revenue to recover total costs, or to BREAK-EVEN. This X value is called the BREAK-EVEN quantity and the corresponding y-value either in the total revenue or total cost equation is the BREAK-EVEN PRICE. These X and Y values are the coordinates of the BREAK-EVEN point.
In the region to the left of BREAK-EVEN POINT, Yc>R, is the LOSS and LOSS= Yc-R.
To the right of BREAK-EVEN POINT is R>Yc, is the PROFIT. PROFIT = R-Yc.
The BREAK-EVEN analysis also includes the concept of CONTRIBUTION MARGIN, C.M. is the difference between the SELLING PRICE PER UNIT and the VARIABLE COST PER UNIT.
Therefore, C.M. (in pesos) = S.P. per unit- V.C. per unit
To express C.M. as a percentage of the selling price per unit: (C.M. in %)(S.P. per unit)= S.P. per unit – V.C. per unit
C.M. in % =[(S.P. per unit-V.C. per unit)/(S.P. per unit)] (100%)
CONTRIBUTION MARGIN is also known as MARK-UP or GROSS PROFIT.
Another method to find the x and y
coordinates of BREAK-EVEN POINT is as
follows:
At the BREAK-EVEN POINT,
R= Yc
(S.P. per unit)x= (V.C. per unit)x+FC
(S.P. per unit- V.C. per unit)x= FC
(Contribution Margin in pesos)x=FC
OR
X or BEP per unit=FC/c.m. in pesos
The Y-coordinate of the BREAK-EVEN POINT,
or the BREAK-EVEN PRICE can be determined
from the preceding formula:
X= FC/ (C.M. in pesos)
X=FC/ (C.M. in %)(S.P. per unit)
X (S.P. per unit) = FC/ (C.M. in %)
THEREFORE, Y or BEP = FC/ (C.M. in %)
The production levels to attain the desired profit, both in units and in pesos, can be obtained by using the contribution margin method.
P= R-Yc
P= (S.P. per unit)X-[(V.C. per unit)X+FC]
P= [(S.P. per unit)X-(V.C. per unit)X]-FC
P+FC=(S.P. per unit- V.C. per unit)X
P+FC=(C.M. in pesos)X
Finally, X= (P+FC)/ (C.M. in pesos)
Where X is the sales volume or production level in units to attain profit.
PESO sales volume to attain P= (P+FC)/ C.M. in %
A practicum group of students in the College of
Business and Economics, majoring in Business
Management and enrolled in the subject
Entrepreneurial research, submits a feasibility study
on the production of garment bags. A summary
report reveals the following projected data analysis
for a particular month:
Rent, administrative salaries, maintenance and
depreciation of industrial sewing machines
amount to P2,160. Material and labor costs
amount to P180 per bag. Mark up is set at 40%.
a) Determine the selling price per unit.
A practicum group of students in the College of
Business and Economics, majoring in Business
Management and enrolled in the subject
Entrepreneurial research, submits a feasibility study
on the production of garment bags. A summary
report reveals the following projected data analysis
for a particular month:
Rent, administrative salaries, maintenance and
depreciation of industrial sewing machines
amount to P2,160. Material and labor costs
amount to P180 per bag. Mark up is set at 40%.
b) How many bags must be sold by the group for
the month in order to break-even.
c) How much will be the revenue or sales at
break-even point?
A practicum group of students in the College of
Business and Economics, majoring in Business
Management and enrolled in the subject
Entrepreneurial research, submits a feasibility study
on the production of garment bags. A summary
report reveals the following projected data analysis
for a particular month:
Rent, administrative salaries, maintenance and
depreciation of industrial sewing machines
amount to P2,160. Material and labor costs
amount to P180 per bag. Mark up is set at 40%.
d) How many bags must be sold to recover fixed
costs?
e) What should be the sales volume in units and
in pesos to obtain a profit of P3,000?
A practicum group of students in the College of
Business and Economics, majoring in Business
Management and enrolled in the subject
Entrepreneurial research, submits a feasibility study
on the production of garment bags. A summary
report reveals the following projected data analysis
for a particular month:
Rent, administrative salaries, maintenance and
depreciation of industrial sewing machines
amount to P2,160. Material and labor costs
amount to P180 per bag. Mark up is set at 40%.
f) Draw the break-even chart.
In each of the equations given below where X
represents quantity and Y as the unit price,
determine which corresponds to a demand curve and
which corresponds to a supply curve, which
corresponds to neither a demand nor a supply curve:
a) 3x+7y+2100=0 d) x-8= 0
b) 8x-5y-400= 0 e) y-5= 0
c) 2x-3y+60= 0 f)(1/2)x+(1/4)y-25 =0
Dynamic Sales Center will supply 50
pocket calculators at Php100 each. The
supply is increased to 80 pieces when
the unit price is increased by 20%. (a)
Set up the supply function. (b) How
many calculators will be supplied if the
unit price is P150? (c) Find the lowest
price at which this item would be
supplied.
The record of sales for Hi-Quality Ware
Products Corporation, which sells plastic
canisters at P50 each, shows a sales volume
of 400 units. The company decides to reduce
the unit price by P15 which consequently
results to sales of 150 more canisters.
(a) Set up the demand function.
(b) What is the highest price to be paid for this
item?
(c) How many canisters would be demanded if
they were free?
Millie’s footwear sells ladies shoes at
P800 a pair. Fixed costs are P120,000 and
variable costs amount to 50% of the total
revenue:
(a) Set up the total revenue, fixed cost, and
total cost functions.
(b) How many pairs of shoes must be sold to
recover fixed costs?
(c) Find the break-even point.
(d) Draw the break-even chart.
For the following equations, where X
represents quantity in thousands of units and
Y represents unit price in hundreds of pesos:
x-y+1 = 0 and 6x+10y-42 = 0
(a) Determine which represents the demand
curve and which represents the supply
curve.
(b) Find the market equilibrium point
algebraically.
(c) Draw the figure.