Download Break-Even Points

Applications and Linear Functions
Example 1 – Production Levels
Suppose that a manufacturer uses 100 lb of material
to produce products A and B, which require 4 lb and
2 lb of material per unit, respectively.
Solution:
If x and y denote the number of units produced of A
and B, respectively,
4 x  2y  100 where x, y  0
Solving for y gives
y  2 x  50
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Demand and Supply Curves
• Demand and supply curves have the following
trends:
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Demand Function
• Relationship between demand amount of
product and other influenced variables as
product price, promotion, appetite/taste, quality
and other variable.
• Q = f(x1,x2,x3,……xn)
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Demand Function
D : Q = a –b P
22
20
18
16
Q
14
12
1
0
100 200 300 400
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500
600
Q
P
20
100
18
200
16
300
14
400
12
500
10
P
600
4
Linear Demand function
Q=a-bP
Q
Q : amount of product
P : product price
b : slope ( - )
a : value of Q if P = 0
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0
P
5
Property of Demand function
1. Value of q and p always positif or >= 0
2. Function is twosome/two together, each value
of Q have one the value of P, and each value
of P have one the value of Q.
3. Function moving down from left to the right
side monotonously
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Supply function
• Relationship between Supply amount of product
and other influenced variables as product price,
technology,promotion, quality and other variable.
• Q = f(x1,x2,x3,……xn)
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Supply Function
S : Q = a +b P
22
20
18
16
14
12
1
0
100 200 300 400
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500
600
Q
P
10
100
12
200
14
300
16
400
18
500
20
600
8
Linear Function Supply
Q=a+bP
Q
Q : Amount of product
P : product orice
b : slope ( + )
a : value of Q if P = 0
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0
P
9
Property of Supply Function
1. Value of q and p always positif or >= 0
2. Function is twosome/two together, each value
of Q have one the value of P, and each value
of P have one the value of Q.
3. Function moving up from the left to the right
side monotonously
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The point of market equilibrium
• Agreement between buyer and seller
directly or indrectly to make the
transaction of product with certain price
and amount of quantity.
• In mathematics the same like crossing
between demand and supply function
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Equilibrium
•
The point of equilibrium is where demand and
supply curves intersect.
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• D: P = 15 - Q
• S :P = 3 + 0.5Q
• A. Determine equilibrium point
• B. Graph D, S function
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Exercise : Price - Demand
At the beginning of the twenty-first century, the world
demand for crude oil was about 75 million barrels per day
and the price of a barrel fluctuated between $20 and $40.
Suppose that the daily demand for crude oil is 76.1
million barrels when the price is $25.52 per barrel and
this demand drops to 74.9 million barrels when the price
rises to $33.68. Assuming a linear relationship between
the demand x and the price p, find a linear function in the
form p = ax + b that models the price – demand
relationship for crude oil. Use this model to predict the
demand if the price rises to $39.12 per barrel.
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Exercise : Price - Demand
Suppose that the daily supply for crude oil is 73.4 million
barrels when the price is $23.84 per barrel and this
supply rises to 77.4 million barrels when the price rises to
$34.2. Assuming a linear relationship between the
demand x and the price p, find a linear function in the
form p = ax + b that models the price – demand
relationship for crude oil. Use this model to predict the
supply if the price drops to $20.98 per barrel.
What’s equilibrium point and make a graph in the same
coordinate axes
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Example 1 – Tax Effect on Equilibrium
p
8
q  50
100
Let
be the supply equation for a
manufacturer’s product, and suppose the demand
equation is p   7 q  65.
100
a. If a tax of $1.50 per unit is to be imposed on the
manufacturer, how will the original equilibrium price
be affected if the demand remains the same?
b. Determine the total revenue obtained by the
manufacturer at the equilibrium point both before and
after the tax.
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Solution:
a. By substitution,
Before tax,
7
8

q  65 
q  50
100
100
q  100
and
After new tax,
8
7
q  51.50  
q  65
100
100
q  90
8
p
(90)  51.50  58.70
100
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and
p
8
100   50  58
100
Solution:
b. Total revenue given by
Before tax
yTR  pq  58100  5800
After tax,
yTR  pq  58.7090  5283
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BREAK EVENT POINT
• BEP is identifying the level of operation
or level output that would result in a
zero profit. The other way thatr the firm
can’t get profit or don’t have loss
• TC= FC + VC
• TC : Total Cost
• FC : Fixed Cost
• VC : Variabel Cost
• VC = Pp x Q = cost production per unit x
•
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amount of product
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• TR = Pj x Q
• Tr : Total Revenue
• Pj : Selling Price
• Q : Amount of product
Profit = TR –TC
BEP  TR=TC
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T
R
$
T
C
profit
C
bep
BE
P
loss
F
C
Q
0
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Q
bep
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Example 2 – Break-Even Point, Profit, and Loss
A manufacturer sells a product at $8 per unit, selling
all that is produced. Fixed cost is $5000 and variable
cost per unit is 22/9 (dollars).
a. Find the total output and revenue at the break-even
point.
b. Find the profit when 1800 units are produced.
c. Find the loss when 450 units are produced.
d. Find the output required to obtain a profit of
$10,000.
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Break-Even Points
•
Profit (or loss) = total revenue(TR) – total cost(TC)
•
Total cost = variable cost + fixed cost
yTC  yVC  y FC
•
The break-even point is where TR = TC.
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Solution:
a. We have yTR
 8q
yTC  yVC  y FC 
22
q  5000
9
At break-even point,
yTR  yTC
22
q  5000
9
q  900
8q 
and
b.
yTR  8900  7200
yTR  yTC
 22

 81800    1800   5000  5000
9

The profit is $5000.
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BEP Exercise
• A firm produce some products where the cost per unit is
Rp 4.000,- and selling price per unit is Rp12.000,.Management developed that fixed cost is Rp 2.000.000,Determine the amount of product where the firm should
sell amount of product so that the break event point
achieved.
• a. Find the total output and revenue at the break-even
point.
• b. Find the profit when 1600 units are produced.
• c. Find the loss when 350 units are produced.
• d. Find the output required to obtain a profit of
Rp 7,000.
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