Question

Find the minimum value of C=-2x+y subject to the following constraints x≥-5 x≤4 y≥-1 x≤3

Answer 1

Answer:

The minimum value of C is -9

Step-by-step explanation:

we have

$C=-2x+y$

$x\geq -5$

$x\leq 4$

$y\geq -1$

$y\leq 3$

using a graphing tool

The solution is the shaded rectangle

see the attached figure

The vertices of the rectangle are the points

$(-5,3),(4,3),(4,-1),(-5,-1)$

To find the the minimum value of C, substitute the value of x and the value of y of each vertex and calculate the value of C, then compare the results

For $(-5,3)$

$C=-2(-5)+3=13$

For $(4,3)$

$C=-2(4)+3=-5$

For $(4,-1)$

$C=-2(4)-1=-9$

For $(-5,-1)$

$C=-2(-5)-1=9$

therefore

The minimum value of C is -9