Buildings higher than 3 floors need to have foundations dug into underground bedrock in order to guarantee long-term stability.  The following table shows the cost of foundations depending on the number of floors that the building would be designed for:

 

#Floors F	Foundation Cost
1≤F≤4	3 M
5≤F≤8	7 M
9≤F≤12	12 M
13≤F≤16	18 M
17≤F≤20	25 M
21≤F≤24	33 M
25≤F≤28	42 M

 

And follows an arithmethic sequence for every four additional floors (52M, 63M, 75M….etc).

 

The per-floor building costs also follow an arithmetic sequence, as you can see from the following table:

Floor number	Marginal Cost		Floor number	Marginal Cost
Ground	4,000,000		7th	2,500,000
Second	3,750,000		8th	2,250,000
Third	3,500,000		9th	2,000,000
4th	3,250,000		10th	1,750,000
5th	3,000,000		11th	1,500,000
6th	2,750,000		12th	1,250,000

 

But from the 13th floor onwards, each additional floor costs exactly Php 1,000,000 to build.  

Sample calculation:   if you decide to produce a six-storey building, then the cost would be 27.25M :     7M (Foundations) + 4,000,000+3,750,000+ …….. +3,000,000+2,750,000 (Building )= 27.25 M

Upon finishing, each of the building units would be sold based on floor area, irrespective of what floor the unit would be on.  What number of floors would have been optimal to maximize the profit for each of the units produced?   

Show your solutions on the Google Sheet link you will submit at the end of the exam.   On the same Google Sheet, provide the total building costs given your chosen number of floors.  Indicate the quantitative variable (Cost? Profit?) used to determine your recommended number of floors.