Question

Question 9 Find the value(s) of the function on the given feasible region. Find the maximum and minimum of z = 8x + 8y. K0,5) (5/2,5) (0,4) (6,0) (10,0) 56,32 80,32 -32,-56 48,40

Answer 1

Question 9: Option 2 : 80, 32

Solution:

$\small z=8x+8y$

At  $\small \left ( 6,0 \right )$

$\small z=8\times 6+8\times 0={\color{Red} 48}$

At  $\small \left ( 10,0 \right )$

$\small z=8\times 10+8\times 0={\color{Red} 80}$

At  $\small \left ( 5/2,5 \right )$

$\small z=8\times \frac{5}{2}+8\times 5=20+40={\color{Red} 60}$

At  $\small \left ( 0,5 \right )$

$\small z=8\times 0+8\times 5={\color{Red} 40}$

At  $\small \left ( 0,4 \right )$

$\small z=8\times 0+8\times 4={\color{Red} 32}$

So, the maximum and minimum value of $\small z=8x+8y$ is $\small 80,32.$