Question

What is the minimum value for z = -x + 3y over the feasibility region defined by the constraints shown above?

Answer 1

Answer:

The minimum value for  $z=-x+3y$  over the feasibility region is -1.

Step-by-step explanation:

Given conditions:

The function  $z=-x+3y$

Subject to the following constraint

$x\geq 1$

$x\leq 7$

$y\geq 2$

$y\leq \frac{-1}{3}x+6$

Graph the region correspond to the solution of the system of constraints as given below.

Now, from the graph we have the coordinates of the vertices of the region formed.

The vertices are $(1,2)$ , $(7,2)$, $(1,5.667)$ and  $(7,3.667)$.

now, evaluate the function  $z=-x+3y$  at each  vertex.

At $(1,2)$,

$z=-1+3\cdot 2=-1+6=5$

At $(7,2)$,

$z=-7+3\cdot 2=-7+6=-1$

At  $(1,5.667)$

$z=-1+3\cdot 5.667=-1+17.001=16.001$

At  $(7,3.667)$

$z=-7+3\cdot 3.667=-7+11.001=4.001$

So. the minimum value of function $z=-x+3y$ over the feasible region is -1.

Answer 2

Minimum value of x = 1
Minimum value of y = 2

Minimum value of z:
z = -x + 3y
z = -1 + 3(2)
z = 5

The answer is A.