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Formulate a system of equations for the situation below and solve.
A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve,
and long-sleeve. The time (in minutes) required by each department
to produce a dozen blouses of each type is shown in the following table.
Sleeveless Short-Sleeve Long Sleeve
Cutting 9 12 15
Sewing 22 24 28
Packaging 6 8 8
The cutting, sewing, and packaging departments have available a maximum
of 73.5, 150, and 44 labor-hours, respectively, per day.
How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity?
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Let x be the number of sleeveless blouses (dozen);
y be the number of short-sleeve blouses (dozen);
z be the number of long-sleeve blouses (dozen).
Write equations as you read the problem
9x + 12y + 15z = 73.5*60 = 4410 minutes
22x + 24y + 28z = 150*60 = 9000 minutes
6x + 8y + 8z = 44*60 = 2640 minutes.
Use the matrix equations solver in your calculator
and get the in the next instance
x= 120 dozen; y= 90 dozen; z= 150 dozen.
Solved.