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38 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

7 / S þ 1D 630 (2:1)
10

Constraint 2:

Hours of sewing Hours of sewing
time used time available
1
From Table 2.1 we see that every standard bag manufactured will require / 2 hour
5
for sewing, and every deluxe bag will require / 6 hour for sewing. Because 600 hours
of sewing time are available, it follows that:

1 / 2 S þ / 6 D 600 (2:2)
5

Constraint 3:

Hours of finishing Hours of finishing
time used time available

Every standard bag manufactured will require one hour for finishing, and every
2
deluxe bag will require / 3 hour for finishing. With 708 hours of finishing time
available, it follows that:

2
1S þ / 3 D 708 (2:3)

Constraint 4:

Hours of inspection and Hours of inspection and
packaging time used packaging time available
1
Every standard bag manufactured will require / 10 hour for inspection and pack-
1
aging, and every deluxe bag will require / 4 hour for inspection and packaging.
Because 135 hours of inspection and packaging time are available, it follows that:

1 1
/ 10 S þ / 4 D 135 (2:4)

We have now specified the mathematical relationships for the constraints associated
with the four departments. Have we forgotten any other constraints? Can the company
produce a negative number of standard or deluxe bags? Clearly, the answer is no.So,to
prevent the decision variables S and D from having negative values, two constraints,

S 0 and D 0 (2:5)

must be added. These constraints ensure that the solution to the problem will
contain nonnegative values for the decision variables and are referred to as the
nonnegativity constraints. Nonnegativity constraints are a general feature of all
linear programming problems and may be written in the abbreviated form:

S; D 0

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