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.
