Doubt on M1W4 Practice assignment Question 4

[Souvik Ghosh]

4. A company’s profitts are known to be dependent on the months of a year. 

(in lakhs of Rupees) from January to December is P(x) = −2x

2 + 25x. Here, x represents

the month number, starting from 1 (for January) and ending at 12 (for December). On this

basis, choose the correct option.

e maximum prot in a month is Rs.78 lakhs.

e maximum prot in a month is Rs.78.125 lakhs.

e maximum prot in a month is Rs.77 lakhs.

e maximum prot is recorded in June.

e prot in December is 144 lakhs.

None of the above.

Solution:

e prot of the company is given as P(x) = −2x

2 + 25x. Observe P(x) is downward

open. So, the maximum prot will be recorded at vertex.

e X-Coordinate of the vertex is x =

−b

2a =

−25

2(−2) = 6.25

So, the vertex lies between the lines x = 6 and x = 7

erefore, the maximum prot will be recorded in the month of June(x = 6) or July(x = 7).

MY QUERY:

++++++++++++++

Here the calculation has been carried out considering month value as Discrete that is why instead of considering 6.25 we are checking discrete value 6 or 7.

But it has been declared in header that month is to be treated as continuous

NOTE:
There are some questions which have functions with discrete valued domains (such as month or year). For simplicity, we treat them as continuous functions.

How do we know in which question it is treated as discrete and where it is continuos.

[Anand Iyer]

which header are you talking about Souvik?

As for the question of when to treat data continuous or discrete, see if this helps...https://stats.stackexchange.com/a/209.  Much depends on the context of the question too.