Find the minimum and maximum values of the objective function and the points where they occur, subject to the constraints x ≥ 0,

y ≥ 0,

x + 5y ≤ 25,

x + y ≤ 18,
and
2x + 2y ≤ 12.
z = x + 6y
The minimum value of
occurs at
(x, y) =

.
The maximum value of
occurs at
(x, y) =

.

Afarmer has a large field that is x feet in length. he wants to fence in a rectangular section in the middle of the field , leaving a length of 100 feet of open field behind each end of the fenced rectangle. he also wants the width of the fenced-in space to be 100 feet less than its length. find the expressions to represent the length and width of the fenced section of the field