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 Short Long- Sleeveless Sleeve Sleeve Cutting Sewing Packaging 12 24 8 15 28 8 The cutting, sewing, and packaging departments have available a maximum of 78, 160, and 48 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 dozen dozen dozen

Answer 1

Tong Short sleeve 12 sleeve is. 28 22 Solved; Sleerelers Cutting Sewing 24 8 Packaging The cutting, sewing and packaging department have available a maxionuon of 78, 160, 48 hours respectively per day. 6 8 Lect; x = number of dozens of sleevless shirts produced = number of dozens of short sleeve shird poroduced Z= number of dozens of long sleeve shirts produced. Maximum time for Cutting avaidlable is 78 hr. = 4680 minutes

(D Nowi Minutee spent cutting sleevless shirt=9x Minutes spon't cutting short sleeve shirts = 12y Minutes spent cutting long sleeve shirt = 152 So we have; 9x+12y + 15z = 4680 Now, again; Maximum time for sewing available is 160 hr. 9600 mintues. Minutes spent sewing sleevless shirt = 22. | Minutes spent sewing short sleeve shirt = 244 Minutes spent sewing long sleeve shirt = 287 So we have; 220+244 +28z = 9600 Again; Max Time for packaging is ush=2880 Minutes spent packaging sleeveless shirt = 60 Minutes spent packagioy short sleeve shirt = By Minutes spent packaging long. deeve shirt = 87 So, we have 6x+84 + 83 = 2880 minutes

So the speten of equcation we must solve is 922 +12y +153 = 4688 22x +2y +283 = 9600 +83 By Gauss Jordan Gliminations, 6x + sy = 2880 12 22. 6 IS 28 8 4680 aboo 2880 8 RiR-9 - ² 24 22 G 5/3 28 & 520 9600 28802 R2 - R2-22 R, 4/3 5/3 520 - 16/3 - 26/3 -26/2 -1840 8 8 2880 6 Rz -) R3 - GR1

513 43 - 16/3 520 - 1840 263 -240 R2 - R2X-3 16 473 53 13/8 520 345 o -2 -240 RRI y R2 60 o 1318 345 o 6 -240 R3 - R3 = (-2) - 60 345 120 LO R - Ri tl 120 o 1318 345 120 o 0

Ra R2 - 13 R3 - B 120 0 150 120 Therefore; x = 120 y = = 150 3= to x= Sleeveless shirts 120 y = - Short sleeve shirts = 150 Long sleeve shirts = 120 Ans ves