SOLUTION: A small band would like to sell CDs of its music. The business manager says that it costs $340 to produce 100 CDs and $500 to produce 500 CDs. (a) Write a linear function to rep

Question 1025831: A small band would like to sell CDs of its music. The business manager says that it costs $340 to produce 100 CDs and $500 to produce 500 CDs.
(a) Write a linear function to represent the cost, $C , of producing n CDs.
(b) Find the slope and the intercept of the graph of the function, and interpret their meaning.
The slope is ___ and it represents _______
The intercept is ___ and it represents _______

(c) How much does it cost to produce 750 CDs?
(d) If the band can afford to spend $900, how many CDs can it produce?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Plot Cost on the vertical axis
Plot number of CDs on the horizontal axis
You are given 2 points: ( n, C )
( 100, 340 )
( 500, 500 )
--------------
Use the general point-slope formula

multiply both sides by

(a)
----------------------
(b)
The slope measures how fast the cost increases
with the number of CDs.
For every 1 new CD produced, the cost increases by
= $.40
----------------
The vertical intercept, where is
$300 is the cost even if no CDs are produced ( fixed cost )
----------------
(c)

$600
--------------
(d)

1500 CDs can be produced
---------------------------
check the equation:
does it go through ( 100,340 ) ?

OK
does it go through ( 500, 500 ) ?

OK
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