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max{e^x+y+z} s.t. {x+y+z=1 x 2 +y 2 +z 2 =1 Find the first-order conditions. Find the point where the objective function reaches its maximum. Find

max{e^x+y+z} s.t. {x+y+z=1

x2+y2+z2=1

  1. Find the first-order conditions.
  2. Find the point where the objective function reaches its maximum. Find the maximum.
  3. If the right-hand-sides of the constraints were instead 1.02 and 0.98, respectively, what is the approximate change in the optimal value of the objective function?

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