break-even analysis (module 3) help with review question

[akay]

hi there !

i seem to be stuck on a review question (seems really simple but i still can't figure it out    )
graphs & relations: break even analysis and some help would be greatly appreciated 
(essential further maths, 4th edition, pg 466 Q21 , if you have the book handy )

The multiple choice question:

The graph opposite shows the cost, $C, of making n apple pies.     
The profit from the sales of 80 apple pies is $100.
The selling price for one apple pie is :

A: $1.50
B: $1.75
C: $2.50
D: $2.75
E: $3.75

(NOTE- the graph in the book is very plain- not even a scale is shown, shows one line with two coordinates: (0,20) [y intercept] and (100,170) [random point on line that book gives].

From this i have been able to work out the gradient [1.5] and thus the cost equation which turns out to be:

C= 1.5n+20 ∴ to produce 80 apple pies it cost $140

However here is the part where i get stuck upon 

I know profit can be calculated by P = Revenue - Cost, but not quite sure how to get the revenue eqn ??

Thankyou in advance ! any advice much appreciated

[fred42]

Revenue = Profit + Cost
I'm not sure you have the correct coordinates of the "random point". I can't see the question but did you choose a point as far to the right as possible?

According to your figures:
Revenue for 80 apples = 140 + 100 = $240
So revenue for one apple = 240/80 = $3.

The closest answer would be D $2.75.

[Stick]

hi there !

i seem to be stuck on a review question (seems really simple but i still can't figure it out    )
graphs & relations: break even analysis and some help would be greatly appreciated 
(essential further maths, 4th edition, pg 466 Q21 , if you have the book handy )

The multiple choice question:

The graph opposite shows the cost, $C, of making n apple pies.     
The profit from the sales of 80 apple pies is $100.
The selling price for one apple pie is :

A: $1.50
B: $1.75
C: $2.50
D: $2.75
E: $3.75

(NOTE- the graph in the book is very plain- not even a scale is shown, shows one line with two coordinates: (0,20) [y intercept] and (100,170) [random point on line that book gives].

From this i have been able to work out the gradient [1.5] and thus the cost equation which turns out to be:

C= 1.5n+20 ∴ to produce 80 apple pies it cost $140

However here is the part where i get stuck upon 

I know profit can be calculated by P = Revenue - Cost, but not quite sure how to get the revenue eqn ??

Thankyou in advance ! any advice much appreciated

Profit = Revenue - Cost
Profit = kn - (1.5n - 20)
100 = 80k - [1.5(80) - 20]
100 = 80k - 120 - 20
100 = 80k - 140
80k = 240
k = 3

Answer should be $3.00 but it's not there! Out of curiosity, what answer does the book provide? Have you given us all of the correct information?

[akay]

the point (100,170) is what's printed in the book, i didn't pick it out or anything.
it's the only point the book actually gives apart from the y-intercept.
the graph is plain, one positive linear line with the two coordinates printed.
The eqn isnt even labelled on the line and there is no scale !

The answer in the back of the book states D: $2.75   

Which confused me. Tried working backwards to figure out how this is but no such luck 

i think it may possibly be a mistake/typo at the back of the book, as this wouldn't be the first time; yet this frustrates me, something so simple yet can't seem to get it right.

thanks for your replies