A 3-sided enclosure along a river, length 1, width w. A farmer uses 170 m of fencing to build three sides of a coop along a river, using the river as the fourth
side.
A. Set a relationship between the length of the fencing and the dimensions of the coop given in the
figure.
170 -
B. Give the area of the coop as a function of the width only.
A(w)
C. Find the dimensions that maximize the area of the coop, and the area of the coop.
w
m
l=
m
A=
m2

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is