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Intersecting lines
Finding the point of intersection of two curves is a form of solving
simultaneous equations.
One example of simultaneous equations is finding a break even point.
This type of question will often involve one equation for the cost of
the goods produced and a second equation for the revenue (or income)
from sales of the goods.
The point at which the 2 lines meet is called the break even point.
At this point the costs equal the revenue.
On one side of this point (normally the left), the costs exceed the
revenue, so there is a loss of money.
On the other side of this point (normally the right), the revenue
exceeds the costs, so a profit is made.
Example 1
Sarah was planning a disco. The cost of hiring the 80’s juke box was
$135 and food for the guest was $5·50 per head. Sarah charged $10
per person to attend.
$
a) Form equations for the cost
Revenue
350
and revenue for the disco.
Revenue
b) Plot the lines
300
c) What is the break even point?
250
a) C = 135 + 5·5n
200
n 0 10 20 40
C 135 190 245 355
150
R = 10n
100
n 0 10 20 40
R 0 100 200 400
50
c) 30 guests
10
20
30
40 n
Example 2
Tim makes greeting cards at home to sell at his retirement village. He
needed to purchase $90 worth of pens and nibs at the start and each
card costs $2·75 in paper and ink to make. Tim sells the cards for $5
$
each.
Cost
a) Form equations for the cost 250
and revenue of the cards.
200
Revenue
b) Plot the lines
c) What is the break even point?
150
a) C = 90 + 2·75n
n 0 8 24 40
100
C 90 112 156 200
R = 5n
50
n 0 10 20 30
R 0 50 100 150
c) 40 cards
10
20
30
40
50 n
Today’s work
Exercise 12B pg 364
#2, 4, 6