maximisation

[Var1995]

i solved it using lagrange but i m not getting any interior pt so (a) will be the right option?

[Dreyfus]

Since there is no non-negativity constraints on x and y and since f is decreasing in y and increasing in x. You can check that by plotting the level curves or otherwise there is no solution. For instance take three bundles

a) (x,y) = (4,-3) this gives f = 7

b) (x,y) = (10,-9) this gives f = 19

c) (x,y) = (100,-99) this gives f > 19

d) there are infinitely many bundles that gives f > 19

Therefore no solution exist.

[Var1995]

thanks