Bombay Palace vs. The Grand Olympia

Which banquet hall provides a better deal?

Introduction

Jonathan McMaster and Lily Kaur are having secular wedding. The couple don't want the wedding to have too many guests with very expensive prices. The couple want a banquet hall that provides good service while the cost being affordable. There are around 200 people coming for the wedding, Jonathan and Lily's budget is $25,000. They research on all the banquet halls in London, they finally decide on 2 banquet halls ; Bombay Palace and The Grand Olympia. But unfortunately Jonathan prefers The Grand Olympia and Lily prefers Bombay Palace, they both are arguing which one is better, we now have to help the couple decide which banquet hall is better and why.

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How do we solve this dispute?

There is a simple way we solve this, by convincing one of them to which is the better banquet hall in terms of cost, seating, and services. We first make a equation with variables correlating to the situation. Second of all, we show them the point of intersection ( where both banquet halls pricing will be the same) to visually show and prove to which banquet hall is better, which one is cheaper, and where do they have the same cost at the same number of people, I will make a graph and table of values. This will be my evidence supporting my argument as to which banquet hall is better. Last but not least, I will conclude my thoughts as to which banquet hall is better for Jonathan and Lily's wedding.

Services and Costs

Bombay Palace

Wedding Package

* Flat fee of $1000

( Flat fee of 1000 dollars due to cost of renting the banquet hall for 1 day)


Standing- 500 persons

Seated- 310 persons

Catering - $80 per person


The Grand Olympia

Wedding Package

*Flat fee of $890

( Flat fee of 890 dollars due to cost of renting the banquet hall for 1 day)


Standing- 500 persons

Seated- 310 persons

Catering- $100 per person

Mathematically Solving this Dispute

We can solve this dispute mathematically between the couple by evidence.


Let c represent the cost and p represent the number of people attending the wedding.


Bombay Palace

There is a flat fee of 1000 dollars with catering of $80 per person.

In mathematical terms, this would look like; c = 80p + 1000.


The Grand Olympia

There is a flat fee of 890 dollars with catering of $100 per person.

In mathematical terms, this would look like; c = 100p + 890.


Ax + By = C

Bombay Palace: -80p + c = 1000

The Grand Olympia : -100p + c = 890

Table Of Values

In this table we have number of people affecting the cost, more people higher prices.
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Point of intersection

The point of intersection is when the two lines intersect. When they intersect, it means that at that point the equations of both lines are equal. We calculate the point of intersection by solving linear systems.


1: y = 80x + 1000

2:y= 100x + 890

We need to find the point of intersection ( or POI for short), hence let us substitute equation 1 to equal to equation 2 to find the value of x ( which is number of people attending the wedding).


80x + 1000 = 100x + 890

80x - 100x = -1000 + 890

-20x/ -20 = -110/ -20

Therefore, x = 5.5. But there is a problem, 5.5 people cannot attend the wedding obviously hence we will, in this context have to round it to 6 people.

To find the cost for "5.5 people" who attend the wedding, we will substitute the value of x in the equation to find the value of y.


y = 80( 5.5 ) + 1000

y = 440 * - This is the cost for "5.5 people" attending, excluding the flat rate since

practically speaking, there are still more people yet to come,but I will

still show the cost including the flat rate.

y = 440 + 1000

y = 1440


Now, I will confirm if the cost is the same at the same number of people for both banquet halls.


Bombay Palace

c = 80p + 1000

1440 = 80( 5.5 ) + 1000

1440 = 440 + 1000

1440 = 1440

Check!


The Grand Olympia

c = 100p + 890

1440 = 100( 5.5 ) + 890

1440 = 550 + 890

1440 = 1440

Check!


X is the number of people attending the wedding because number of people attending the wedding are independent of the cost of the wedding while the cost depends on the number of people who attend the wedding (y).


* Unfortunately the point of intersection on the graph is very early on, thus I couldn't actually show the intersection properly with same rate of data because even if I tried no software was allowing me to input that much amount of data, that's why just to show where they intersect early on in the graph I labelled 5.5 ( around 6 people where the 2 lines meet and have the same cost for the same number of people).

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Conclusion

I conclude based on my findings through graphs and my table of values that Bombay Palace has the best deal with same number of people standing or seated as The Grand Olympia. Both graphs have the same cost at around 6 people, but after that The Grand Olympia's line goes up drastically. Both banquet halls were under the budget and had the same number of seating and standing but Bombay Palace had the least expensive price of $17,000 while on the other The Grand Olympia was charging around $20,890. Obviously, if the couple want a secular wedding with least expensive prices, with choice of either Bombay Palace and The Grand Olympia, I would advise both of them to go for Bombay Palace.