Algebra and graphing

[Cyprus]

Can you guys tell me if this is correct?

Joanne sells silk-screened t-shirts at a community festival. Her marginal cost to produce one t-shirt is $3.50. Her total cost to produce 60 t-shirts is $300, and she sells them for $7 each. Graph this information and determine the number of t-shirts Joanne must produce and sell to break even.

x is the number of t-shirts
f is the fixed cost
300 = 3.50*60 + f
90 = f
The line for her cost: C = 3.50x + 90
Revenue: R = 7x
The break-even point is where those lines meet.
3.5x + 90 = 7x
90 = 3.5x
25.7 = x
So she needs to sell 26 t-shirts to make a profit.

 

[Deleted member 4993]

Can you guys tell me if this is correct?

Joanne sells silk-screened t-shirts at a community festival. Her marginal cost to produce one t-shirt is $3.50. Her total cost to produce 60 t-shirts is $300, and she sells them for $7 each. Graph this information and determine the number of t-shirts Joanne must produce and sell to break even.

x is the number of t-shirts
f is the fixed cost
300 = 3.50*60 + f
90 = f
The line for her cost: C = 3.50x + 90
Revenue: R = 7x
The break-even point is where those lines meet.
3.5x + 90 = 7x
90 = 3.5x
25.7 = x
So she needs to sell 26 t-shirts to make a profit.

Your calculations are correct.

However, my interpretation of your given problem is that you are required to solve it graphically.

 

[Cyprus]

Thanks Subhotosh,

I was thinking I could graph these two equations

C = 3.50x + 90
Revenue: R = 7x


And the point where they meet will be her break even point. (which is 25.71)

I was a little confused because one of my friends solved the problem like this:
P=R-C
She sells shirts @7 a piece, R=7
So, P=7s-3.5s-60
P=1.5s-60
In order for her to break even (profit is 0)
0=1.5s-60
s=40
Since we cant have fractions of shirts we say she needs to sell 23 to break even

Which process makes more sense to you guys, I personally am a little lost on how she got to 23 shirts to break even.