Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Given the objective function f(x,y)=5x-2y and the vertices W(3,4),X(-6,8), Y(7,-3) and Z(2,-10), which point gives the maximum value of func?

* Y

* Z

* W

* X

2 Answers

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  • 1 month ago
    Favorite Answer

    Linear programming theory says that optimal values for the objective function must occur at the vertices of the feasible region.

    f(3,4) = 5(3) - 2(4) = 15 - 8 = 7

    f(-6,8) = 5(-6) - 2(8) = -30 - 16 = -46

    f(7,-3) = 5(7) - 2(-3) = 35 + 6 = 41

    f(2,-10) = 5(2) - 2(-10) = 10 + 20 = 30

    Looks like (7,-3) gives the maximum value which is point Y.

  • TomV
    Lv 7
    1 month ago

    f(W) = f(3, 4) = 5(3) - 2(4) = 15-8 = 7

    f(X) = f(-6, 8) = 5(-6) - 2(8) = -30 - 16 = -46

    f(Y) = f(7, -3) = 5(7) - 2(-3) = 35 + 6 = 41

    f(Z) = f(2, -10) = 5(2) - 2(-10) = 10 + 20 = 30

    f(Y) = 41 is the maximum value over the given vertices.

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