Simarpreet's Corporate Party

Welcome to Embassy Grand Banquet Hall!

This is a world-renowned banquet hall for multiple events, even seminar conferences, and business meetings. In this location, you will feel very comfortable and will be treated like royalty.

Offers Available to choose for a Corporate Party

Offers:
• Gold Plus09 which includes a flat fee(initial cost) of \$800 and \$50/guest that attends.
• Gold Plus10 which includes a flat fee(initial cost) of \$600 and \$60/guest that attends.

Gold Plus09 Offer!

• Gold Plus09
C=Total Cost for the event
n=Number of Guests
800 is the initial cost/flat fee
C=50n+800------- Y=mx+b form(Slope y-intercept)
50n-C=800-------Ax=By=C form(Standard Form)
50n-C-800=0------Ax+By+C=0 form(Standard Form)

Gold Plus10 Offer!

• Gold Plus10

C=Total Cost for the event

n=Number of Guests

600 is the initial cost/flat fee

C=60n+600------- Y=mx+b form(Slope y-intercept)

60n-C=600-------Ax=By=C form(Standard Form)

60n-C-600=0------Ax+By+C=0 form(Standard Form)

Below are both the offers(situations) graphed

Red Line on the graph represents the Gold Plus10 Offer.

Green Line on the graph represents the Gold Plus09 Offer.

They are graphed in "slope y-intercept form"(Y=mx+b).

Red Line-Gold Plus10 OFFER

Blue Line-Gold Plus09 OFFER

Well...How much is this going to cost me? I am confused between which offer to choose!

In this graph above, the two lines are intersecting at points (20, 1800), which represents the cost of the event(\$1800) with a total number of 20 guests.

Why are these lines intersecting?

These lines are intersecting because the two options to choose from eventually meet at a point on the graph where the value is the same(I.e. guests=20 and cost=\$1800). The graphical equations to explain this are:

For example:

Now I am going to choose two points for each line on the graph;

Red line- (0,600) and (20,1800)

Blue Line- (0,800) and (20,1800)

Y2-Y1 / X2-X1= 1800-800/20-0= 50

AND

Y2-Y1 / X2-X1= 1800-600/20-0= 60

*The bolded answers are the slope.

Now, the equations are:

Since the equations are in Y=mx+b form(Slope y-intercept form)

m=slope

b=initial value(y-intercept)

y=total cost(in context)

So…

Red Line: C=50n+800

Blue Line: C=60n+600

To determine that the equation makes sense, substitute 20 into "n" and "1800" into "C", and make sure that the equation is correct

1800=60(20)+600=1200+600=1800

1800=50(20)+800=1000+800=1800

Graphical Equations(2nd set):

Blue Line: C=60n+600

Red Line: -10, 600 are the x and y intercepts respectively. Now, the equation is:

x+90y=1800

Both of the equations need to verify that the point of intersection is (20,1800) as it is displayed on the graph previously in this document.

x+90y=1800---x+90(0)=1800---x=1800

and

x+90y=1800---0+90y=1800---90y/90=1800/90=20

Therefore, the point of intersection is (20,1800)

-10+600=590 therefore this is correct, and now 50n+600=C, so the slope is 50 and the y-intercept is 600, therefore, if we graph these points, as shown below, we will get the point (20, 1800) as the point of intersection.

Equations: 50n+600=C or C=50n+600 and also x+90y=1800. Below is a Graph showing this "point of intersection":

What does it all add up to? What do you conclude from this?

To decide which offer to choose, it will completely depend upon the fact of how many guests you are inviting to your corporate party. As you can observe from the graph above and the previous graph, the GoldPlus09 Offer is more suitable and at a cost much more efficient than the GoldPlus10 Offer because if you were to invite more than 20 people to the party, then this offer would suit you best as it is cheaper than the other offer after the point of 20 guests @ a cost of \$1800. If you observe both offers, the Gold plus09 offer has \$1720 as the cost for 19 people whereas the GoldPlus10 offer has \$1750 , which shows us that the Gold Plus09 offer is better than the other before inviting 20 people. If you invite 20 people, then the cost is the same so at that point it does not matter what offer you choose. Otherwise if you would like to invite guests that are under the amount of 20, then the GoldPlus10 offer would work best for you because it is more cheaper at this point of time. Another way this can be proven is if you observe the data tables for both the offers. Gold Plus09 offer has a total cost of \$25,800 @ 500 guests whereas Gold Plus10 offer has a total cost of \$30, 600 @ 500 guests. Now, just to sum up, if you are inviting 20 guests to your party, it does not matter what offer you choose because the cost will be the same, and if more then, the Gold Plus09 Offer will suit you best, otherwise Gold Plus10.