College Algebra 9th txtbk

16 CHAPTER 7 SYSTEMS OF EQUATIONS AND MATRICES
SOLUTION
To organize all of the information provided, a table is helpful.
Maximum
Standard Model Competition Model Labor-Hours
(labor-hours (labor-hours Available
per board) per board) per Week
Fabricating 6 8 120
Finishing 1 3 30
Let
These variables are restricted as follows:
Fabricating department restriction:
Finishing department restriction:
x Number of standard boards produced per week
y Number of competition boards produced per week
Weekly fabricating time Weekly fabricating time
labor-hours
a b a b aMaximum b
for x standard boards for y competition boards available per week
6x 8y 120
Weekly finishing time
finishing time
a b aWeekly
for x standard boards for y competition boards b Maximum labor-hours
a b
available per week
1x 3y 30
Since it is not possible to manufacture a negative number of boards, x and y also must
satisfy the nonnegative restrictions
© Corbis RF
x 0
y 0
The production levels x and y must satisfy the following system of linear inequalities:
6x 8y 120
x 3y 30
x 0
y 0
Fabricating department restriction
Finishing department restriction
Nonnegative restriction
Nonnegative restriction
Graphing this system of linear inequalities, we obtain the set of feasible solutions, or
the feasible region, as shown in Figure 10. For problems of this type and for the linear programming
problems we consider in the next section, solution regions are often referred to
as feasible regions. Any point within the shaded area, including the boundary lines, represents
a possible production schedule. Any point outside the shaded area represents an
impossible schedule. For example, it would be possible to produce 12 standard boards and
5 competition boards per week, but it would not be possible to produce 12 standard boards
and 7 competition boards per week (see the figure).