Homework SourseFormulate a system of equations for the situation below and
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.
The cutting, sewing, and packaging departments have available a maximum of 93, 188, and 56 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?
| Sleeveless | Short- Sleeve | Long- Sleeve | |
|---|---|---|---|
| Cutting | 9 | 12 | 15 |
| Sewing | 22 | 24 | 28 |
| Packaging | 6 | 8 | 8 |
Solution
three types of blouses: sleeveless, short-sleeve, and long-sleeve be x, y , z
The cutting, sewing, and packaging departments have available a maximum of 93, 188, and 56 labor-hours, respectively, per day.
plant is operated at full capacity
Cutting : 9x +12y +15z = 93*60 ----(1)
Sewing : 22x +24y + 28z = 188*60 ---(2)
Packaging : 6x + 8y +8z =56*60 ----(3)
Solve the three equations to get x, y, z
on solving we get : x= 120 (sleeveless); y = 150 (short-sleeve) ; z=180 (long-sleeve)
