Formulate a system of equations for the situation below and solve. A manufacture
ID: 3169097 • Letter: F
Question
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 87, 176, and 52 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
Explanation / Answer
Variable
no. of blouses in dozen for sleeveless = b
no. of blouses in dozen for short sleeve= s
no. of blouses in dozen for long sleeve = l
constraints
1. b,s,l should be non-negative integers
2. total cutting time should not exceed 87, 18s+24s+45l <= 87
3. total sewing time should not exceed 176, 44s+48s+84l <= 176
4. total packaging time should not exceed 87, 12s+16s+24l <= 52
objective
complete capacity of all the dept. are used.
capacity utilization short = (18s+24s+45l - 87) + (44s+48s+84l - 176) + (12s+16s+24l - 52) = 0
solution
0
so answer is sleeves 2 dozens
short sleeves = 2 dozens
long sleeve = 3 dozens
Sleeveless Short-sleeve Long- sleeve Total spent Total available constraint optimal qt. 2 2 3 Per piece time Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 Total time Cutting 18 24 45 87 87 0 Sewing 44 48 84 176 176 0 Packaging 12 16 24 52 52 0 Objective is to get the no. of labor hours of each activity is fully used.0