Question

When Neil Simon opens a new play, he has to decide whether to open the show on Broadway or off Broadway. For example, he decided to open his play London Suite off Broadway. From information provided the following equations were developed:
48,500x-y=1,295,000
27,000x-y=440,000
x represents the number of weeks that the show has run and y represents the profit or loss from the show. The first equation is for Broadway, and the second is for off Broadway.(a).Solve the system of equations to determine when the profit or loss from the show will be equal for each venue.
b.which venue isfavourable

Answer 1

\[48500x - y = 1295000\]\[27000x-y = 440000\]
We have two equations in two unknowns. Because \(y\) has an identical coefficient in both equations, it will be easy to solve by eliminating \(y\). We can either multiply one equation by -1 and add the two equations together, or subtract one equation from the other as is. I prefer to add, so that's what I'll do here:

\[~~~48500x-y = ~1295000\]\[-27000x+y = -440000\]------------------------\[~~~21500x + 0y = ~855000\]Can you solve that for \(x\)?

Answer 2

YES .X IS 39.76 THUS I MADE IT 40 WEEKS

Answer 3

Good. how about the second part?

Answer 4

BUT wat im confused about is ...WHat is the amount of that profit or loss

Answer 5

the second part of the first question.

Answer 6

the value of \(y\) is the profit or loss for that theater if the show has been open for \(x\) weeks.

Answer 7

if you plug in \(x =0\) (show hasn't opened yet), you can see that the Broadway theater must have much higher costs:
\[48500(0) - y = 1295000\]\[y = -1295000\]
\[27000(0)-y = 440000\]\[y = -440000\]

On the other hand, the Broadway theater makes more money each week (the coefficient of \(x\) is almost twice that of the off-Broadway location)

Answer 8

so this is the answer for b?

Answer 9

What can you conclude looking at the graph?

Answer 10

instead of "makes more money" I suppose it would be more accurate to say "brings in more money"

Answer 11

Which theater is more profitable depends on how long the show is going to run. Neither theater makes a profit before quite a few weeks have gone by. You could find the exact value by setting \(y = 0\) (no profit, no loss) and solving for \(x\) for each theater, but looking at the graph, it looks like about 15 or 16 weeks for off-Broadway productions, and 27 or 28 weeks for Broadway productions. After that, it's all gravy. Between those two points, the show is profitable only off-Broadway. Beyond the point at which the two lines cross, the Broadway show is more profitable.

Answer 12

16.3 weeks for an off-Broadway show to turn profitable, 26.7 weeks for the Broadway show to turn profitable.

Answer 13

actually with the second part of question A, i substituted the 40 weeks in each venue equation to find the amount of that profit or loss .does that mean im wrong?

Answer 14

that only tells you how much profit or loss at 40 weeks...

Answer 15

I would probably keep the answer exact and not round it to 40 weeks, myself.

Answer 16

it does ask when the profit or loss will be equal.

Answer 17

so i need to leave it as 39.7 ?

Answer 18

I'm just saying what I personally would do. part a) asks "... to determine when the profit or loss from the show will be equal for each venue."

I would give the value I computed to 1 decimal place, I suppose.

Answer 19

My reading of part b) is they want you to discuss the character of the system like I did.

Answer 20

oh ok i c where the confusion is coming from now.lol

Answer 21

actually there is a second part of the question for A which i accidentally omitted.

Answer 22

if you think the show might be a real flop, and not even earn back its costs, off-Broadway is better because the costs are lower :-)

Answer 23

it says...WHAT IS THE AMOUNT OF THAT PROFIT OR LOSS?

Answer 24

okay. so, at the point where they are equal, what is the value of y?

Answer 25

yes

Answer 26

you take the value of x you found, plug it back into one of the equations, and solve for y.

Answer 27

make sure you correctly label it as a profit or loss, too!

Answer 28

let me plug and let u know wat i got

Answer 29

sounds good

Answer 30

i had 635300

Answer 31

is it a profit or a loss?

Answer 32

I got 633721. It's a positive number, so it is a profit. Remember, when we set x=0, we got y = -1295000 or y = -440000, so the equation gives us a negative number for a loss and a positive number for a profit.

Answer 33

$633720.93 if you want to quibble over a few cents :-)

Answer 34

so the most favourable is off broadway?

Answer 35

well, no, like I said, it depends how long the show will run! an off-Broadway show gets to profitability sooner, and costs less to mount. on the other hand, a Broadway show will make you more money in the long run, if the run is long enough.

Answer 36

how did u get 633721? cos if we plug the x week thus 39.8 into lets say the first equation ypu will get 635300

Answer 37

I solved it exactly.

\[ 21500x+0y= 855000\]\[x = \frac{855000}{21500}\]Plugging into the original equation
\[48500(\frac{855000}{21500}) -y=1295000\]\[y = 48500(\frac{855000}{21500})-1295000 \]\[= 48500*855000/21500 - 1295000 \]\[= 633720.93\]

Answer 38

well said.

Answer 39

so that means for the answer i would need to work out for both the profit and the loss right?

Answer 40

you already have them. that handsome number there is the profit at the point where both theaters have earned the same amount.

Answer 41

oh ok kuul.fankew

Answer 42

you're welcome. now go watch "The Producers" on Netflix :-)

Answer 43

lol ok