# Thread: Problems in GATE preparation and discussion and their solutions

1. ## Problems in GATE preparation and discussion and their solutions

Question :- The cost function for the product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of rs 50 per unit. The number of units to be produced to maximize the profit is
A) 5
B) 10
C) 15
D) 20

2. ## Re: Problems in GATE preparation and discussion and their solutions

Well, i think answer must be 5. As profit = selling price - production cost. So in all 4 cases, profit will be as follows :
1.) Profit = (5 x 50) - (5 x 5 x 5) = 125
2.) Profit = (10 x 50) - (5 x 10 x 10) = 0
3.) Profit = (15 x 50) - (5 x 15 x 15) = - 375
4.) Profit = (20 x 50) - (5 x 20 x 20) = 0

And i have done mech engineering 7 years before so may be i am wrong in above given approach as trying such question after a long time...

3. ## Re: Problems in GATE preparation and discussion and their solutions

Basically u r checking it by the options, but by your approach I got an idea how to solve it.
Assume no. of units as 'x'
so, profit = 50x - 5x2
so differentiate it to maximize.

---------- Post added at 05:05 PM ---------- Previous post was at 05:01 PM ----------

Everybody is invited for their doubts and problems in civil engineering, either numeric or theoretical..!!

4. ## Re: Problems in GATE preparation and discussion and their solutions

you are absolutely right that by differentiation we can get answer directly (50 = 10x)...anyways.....that's the beauty of objective questions....

5. ## Re: Problems in GATE preparation and discussion and their solutions

Choose the grammatically INCORRECT sentence:

The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum.

This country’s expenditure is not less than that of Bangladesh.

They gave us the money back less the service charges of Three Hundred rupees.

This country’s expenditure on educational reforms is very less

6. ## Re: Problems in GATE preparation and discussion and their solutions

Plz give the answer of this question....

7. ## Re: Problems in GATE preparation and discussion and their solutions

The answer to this problem is D.
I think the mistake is in 'very less' but I am not sure.
And if u know the reason then explain.

8. ## Re: Problems in GATE preparation and discussion and their solutions

May be "The answer to this question is A"
"funding" is incorrect ,fund should be mentioned here instead of funding.

9. ## Re: Problems in GATE preparation and discussion and their solutions

Answer is definitely D, as I checked it from the answer keys also. And all the four statements are focussing mainly on 'less'. So considering that we have to check keeping it in context.