The maximum value of z in the following equation z - 6xy-y2 - where 3x-4y - 100 and 4x- 3y - 75 for x -0 and y - 0 is

X≥0 ,y ≥ 0 4x+ 3y ≤ 75 3x+4y ≤ 100 Plotting the lines Checking z = 6xy+y^2 at (0, 0), (0, 25) and (754, 0) z_1 = 0 z_2= 625 z_3= 0 Hence, the maximum value o ...

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Standard XII

Mathematics

Equation of Circle with (h,k) as Center

The maximum v...

Question

The maximum value of $z$ in the following equation $z = 6 x y + y^{2},$ where $3 x + 4 y \leq 100$ and $4 x + 3 y \leq 75$ for $x \geq 0$ and $y \geq 0$ is

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Solution

$x \geq 0, y \geq 0$
$4 x + 3 y \leq 75$
$3 x + 4 y \leq 100$
Plotting the lines

Checking $z = 6 x y + y^{2}$ at $(0, 0), (0, 25)$ and $(\frac{75}{4}, 0)$
$z_{1} = 0 z_{2} = 625 z_{3} = 0$
Hence, the maximum value of $z$ is $625.$

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The maximum value of z in the following equation z=6xy+y2, where 3x+4y≤100 and 4x+3y≤75 for x≥0 and y≥0 is

x≥0,y≥0 4x+3y≤75 3x+4y≤100 Plotting the lines Checking z=6xy+y2 at (0,0),(0,25) and (754,0) z1=0z2=625z3=0 Hence, the maximum value of z is 625.

The maximum value of $z$ in the following equation $z = 6 x y + y^{2},$ where $3 x + 4 y \leq 100$ and $4 x + 3 y \leq 75$ for $x \geq 0$ and $y \geq 0$ is

$x \geq 0, y \geq 0$
$4 x + 3 y \leq 75$
$3 x + 4 y \leq 100$
Plotting the lines

Checking $z = 6 x y + y^{2}$ at $(0, 0), (0, 25)$ and $(\frac{75}{4}, 0)$
$z_{1} = 0 z_{2} = 625 z_{3} = 0$
Hence, the maximum value of $z$ is $625.$