I would use Lagrange multipliers. We have the objective function:
subject to the constraint:
Thus, we get the system:
which implies:
Substituting into the constraint, we find:
Greetings.
Small problem,
Q) We have U=(x^0.5)*y
10y+4x^2=400
and therefore, x=(40-2.5y)^0.5
Goal is to find the units of y to maximize this the value of output.
What I did:
x=40-2.5y^0.5
du/dy = [(40-2.5y^0.5)]^0.5 * y
0=1/4(40-2.5y)^-3/4 * y (2.5)
0=2.5y/(40-2.5y)^3/4
The working seems incomplete but no matter what I do, I keep ending up with y=0. The answer is 3.20. How would we get this?
Thank you for any help.
Thank you for the assist Mark. However, the course I'm taking does not use those methods above so it is not expected from us. Therefore I believe the solution could be found another way. Let me illustrate what I did another similar question:
Q) V=54x+2y^2
y=(280-x^3)^0.5
Find the maximum value of x.
V=54x+2[(280-x^3)^0.5]^0.5
V=54x+560-2x^3
dv/dx = 54-6x^2 =0
6x^2=54
x=3
With the original question, I just have to find y using the equation given in x. I hope this helps.