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So, the optimal point is located at x = 9/5, y = -1/5, with λ = 8/5, and f(x, y) = 4. give these in 3dp

Question

So, the optimal point is located at

x = 1.800,
y = -0.200,
λ = 1.600,
and f(x, y) = 4.000.

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Solution

To express the given values to three decimal places, we need to convert each fraction into a decimal format.

  1. Convert x=95 x = \frac{9}{5} : x=95=1.8 x = \frac{9}{5} = 1.8

  2. Convert y=15 y = -\frac{1}{5} : y=15=0.2 y = -\frac{1}{5} = -0.2

  3. Convert λ=85 \lambda = \frac{8}{5} : λ=85=1.6 \lambda = \frac{8}{5} = 1.6

  4. Convert f(x,y)=4 f(x, y) = 4 : f(x,y)=4.000 f(x, y) = 4.000

Final Answer

The values rounded to three decimal places are:

  • x=1.800 x = 1.800
  • y=0.200 y = -0.200
  • λ=1.600 \lambda = 1.600
  • f(x,y)=4.000 f(x, y) = 4.000

This problem has been solved

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