Question

ables from two resources-laborat h Solve LDS TUT The Pinewood Furniture Company produces chairs and tables from two mnany has 80 hours of labor and 36 board-ft. of wood available each do for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board. whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from chair is $400 and from each table, $100. The company wants to determine the number of che and tables to produce each day to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

Answer 1

solution ! a Let xi be a time required - X2 be a time required for a for a chairs tables. I labor (x) chairs 8 (x2) Tables! 2 wood 10 .6 lavability 80 36 profit = 400 x1 + 80022 Lineas programming model is maximize sub to - 400xit 100 a2 8x1 + 10x2 580. 2X1 + 622 5 36 216 2170, $27,0.. by solve using graphically. > 8+1012 = 80 2120 - 12 = 80 2-0 =21280 210 (10.8) 22+672 = 36 Dico 22- 3 -6 . 7220 → 2-36 18 (1816)

21610) PI exit lox2486 dach (3.276 224+6x2 536 (610) + OJ I 2 3 4 5 of 7 8 9 10 12 13 14 15 16 17 18 821 + 102280 at=6 - ega put in 8x + 10x680 8X6. not 10x2=80 x2 =8048 8 то - 213 BLS 3.2 (3.2, 6) 82 +10 72 = 80 22, +672 = 36 --(X4) 884 + 10x2 = 80 821 +2482=144 - 1422 = -64 x2=64 12=4.57

x2 = 84.57 put in ear o 821 + 10x4.57 = 80 821 = 34.28 21 = 4.28 (4.28, 4.57) We maximize the 2=400 x + 100 x2 (21, 22) 10,0) 10.6) (4.28, 4.57) 2 (6,3.2) (6.0) 2=400 + 100 x2 2=0 2=600 2=2169 2=2720 2 = 2400 we get 2=2720 is maximum at x = 61X2=3.2 6 chairs and and se maximum profit is 2720 when . 3.2 tables are produced.