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.

	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 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	dozen
short-sleeve	dozen
long-sleeve	dozen

Answer 1

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

		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

so answer is sleeves 2 dozens

short sleeves = 2 dozens

long sleeve = 3 dozens