i am having trouble with the assignment.?

Find the maximum value of :

f (x,y) = x + 2y + 3z

s.t. x ? y + z = 1

and x2 + y2 = 1

2.???????? Solve the following problem:

??????????? max f(x,y) = xy

??????????? s.t. ????? x + y2 ? 2

??????????? and ???? x, y ? 0

Note that the global maximum exists for a continuous function on a closed and bounded set, so you just have to find it, not prove its existence.

3.???????? Consider the problem:

??????????? Max U (x, y) = 100 – (x – 1)2 – y2

subject to: x2 + y2 ? 4

Prove that U (x, y) is concave. Write down the Kuhn-Tucker conditions for the solution of the problem. Find the possible solution(s).

4.???????? Solve the differential equations with explicit solutions and intervals of validity:

?

Assignment # 4
ECON 2400A Winter 2016
Instructor: M. Vesselovsky
Distributed: Mar 31
1.

Due: April 7

Find the maximum value of :
f (x,y) = x + 2y + 3z
s.t. x ? y + z = 1
and x2 + y2 = 1

2.

Solve the following problem:
max f(x,y) = xy
s.t.
x + y2 ? 2
and
x, y ? 0
Note that the global maximum exists for a continuous function on a closed and
bounded set, so you just have to find it, not prove its existence.

3.

Consider the problem:
Max U (x, y) = 100 – (x – 1)2 – y2
subject to: x2 + y2 ? 4
Prove that U (x, y) is concave. Write down the Kuhn-Tucker conditions for the
solution of the problem. Find the possible solution(s).

4.

Solve the differential equations with explicit solutions and intervals of validity:

a)

b)

c)