Question 407906: A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is $5,000 and it costs $0.60 to produce each tape. The selling price is $2.00 per tape. How many tapes must be produced and sold each week for the company to generate a profit?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A company manufactures and sells blank audiocassette tapes.
The weekly fixed cost is $5,000 and it costs $0.60 to produce each tape.
The selling price is $2.00 per tape.
How many tapes must be produced and sold each week for the company to generate a profit?
:
Let x = no. of tapes produced
:
The cost to produce these tapes would be:
C(x) = .60x + 5000
:
The revenue from the sales of these tapes which sell for $2, would be:
R(x) = 2x
:
We know to make a profit, revenue has to exceed the costs, right?
R > C
replacing these with the equations we have find x
2x > .60x + 5000
2x -.6x > 5000
1.4x > 5000
x > 
x > 3571.4, has to be an integer, round it up so we have
x = 3572 tapes will produce a slight profit
;
:
Prove that
R = 2(3572) = $7,144.00
:
C = .6(3572) + 5000
C = 2143.20 + 5000
C = $7,143.20
:
revenue exceeded cost by 80 cents!
:
You can see, when 3572 (or more) tapes are produced, a profit will be made
:
Did this make sense to you?
|
|
|
