consumer surplus- please help!

[Xiang]

Quasimodo consumes earplugs and other things. His utility
function for earplugs x and money to spend on other goods y is given by
u(x; y) = 100x − x^2/2+y

Suppose that Quasimodo has $4,000 in total to spend a month. What
is his total utility for earplugs and money to spend on other things if the
price of earplugs is $50?

Please solve. whats the answer?

[Do bats eat cats?]

I'm not sure how consumer surplus is related to this question.

I simply maximised his utility subject to his constraint, and then calculated his utility for those values of x and y.

Mathematically Max U = 100x - x^2/2 + y
               Subject to  : 50x + y = 4000

Solving this gives x=50 and y=1500
and U(50,1500)= 100(50) - (50)^2/2 + 1500 = 5250, which should be the answer you're looking for.

[yushi.]

do bats eat cats? have u used lagrange?

[Do bats eat cats?]

Yeah, you can use the Lagrangian, but for problems where the constraint isn't too complicated, I simply use substitution.

Just substitute y = 4000 - 50x in the utility function. The answer is the same either way.

[Xiang]

I hve been making that consumer surplus triangle for so long :/

[yushi.]

oh yeah substituting...
lagrangian gets very tedious for this one..
thanx.