Question

1. Latex, Inc. has cutting machines, sewing machines, and a supply of latex with which they make rain boots, galaxy dresses, and batman costumes. It takes 10 minutes on a cutting machine, 40 minutes on a sewing machine, and 20 square feet of latex to make rain boots. It takes 20 minutes on a cutting machine, 10 minutes on a sewing machine, and 40 square feet of latex to make a galaxy dress. It takes 50 minutes on a cutting machine, 50 minutes on a sewing machine, and 100 square feet of latex to make a Batman costume. Furthermore, suppose that there are 600 minutes available on the cutting machines, 810 minutes on the sewing machines, and 1800 square feet of latex. There is a profit of $22 on rain boots, $15 on galaxy dresses, and $50 on batman costumes. Set up and solve the linear program to obtain maximum profit from the available resources.

Answer 1

let ni denotes number of rain boots are made let wa denotes number of galaxy dresses are made 13 denotes number of but men costumes are LPP is mode Max 2 - 22x, + 15 m2 + 5013 10x + 20na + 50 13 L 600 nor, & loka + 50 x3 1810 20x, & horat 100 83 L 1800 21, na, 937,0 Standard Form Max 2 22x, & 15x2 + 50hz + o. Si to.sato. S 8. 10%, + 20% + 509 + S1 -600 you, tlong +50 na +52 = 810 20x +yona + 100 kg AS3 1800 xo, no, no, S. ,S2, 337,0

Simplex Tabte 18 ا 15 50 o e CB Basis X3 S 2 S3 b ot Si 16 20 150 1 0 600 (12) - Чо 10 50 0. Sa S3 0 810 8115 20 0 4o 100 0 1 1800 18 0 0 0 0 2 (4-2) 22 15 50 0 o O SC 15 50 O O CB Basis na Na Si 32 150 S3 /blo 50 23 - 25 15 o 60 1 - 130 1210 17 - S3 o - 60o 0 20 50 0 R-5 -100 2j 10 - 2j 112 1. са Basis 50 CB 22 Na si sa S3 56 Mis O 7/15 2/75 - 1/50 0 53/5 22 21 - / -1/30/30 o S3 O 600 16 50 25 c=2jlo -2 315 - 3/5 215 o -025 0

ape (y-2) 20. Henie optimality achieved at 211 = 7 H2 = 0,213 53 N 684