System of equations and inequalities

OPEN ENDED Give a system of equation that is more easilysolved by substitution and a system of equations that is more easilysolved by elimination.OPEN ENDED Write an example of a system of three equations inthree variables that has (-3, 5, 2) as a solution. Show that theordered triple satisfies all three equations.

Writing in Math Use the information about buoy tenderson page 158 to explain how linear programming can be used in schedulingwork. Include a system of inequalities that represents the constraintsthat are used to schedule buoy repair and replacement and an explanationof the linear function that the buoy tender captain would wish tomaximize.

For #4, page 158 is in the attachment.

The U.S. Coast Guard maintains
the buoys that ships use to
navigate. The ships that service
buoys are called buoy fenders.
Suppose a buoy tender can carry
up to 8 replacement buoys. The
crew can repair a buoy in 1 hour
and replace a buoy in 24 hours.
Maximum and Minimum Values The buoy tender captain can use a
system of inequalities to represent the limits of time and replacements on
the ship. If these inequalities are graphed, the points in the intersection
are combinations of repairs and replacements that can be scheduled.
The inequalities are called the constraints. The
intersection of the graphs is called the feasible
graph of
region. When the graph of a system of
constraints
constraints is a polygonal region like the one teasible
region
graphed at the right, we say that the region is
bounded.
vertex |
Since the buoy tender captain wants to service the maximum number of
buoys, he will need to find the maximum value of the function for points
in the feasible region. The maximum or minimum value of a related
function always occurs at a vertex of the feasible region.