Simplex method: using simplex tableau

Discrete Math B: Chapter 4, Linear Programming: The Simplex Method 11 Example 5: Solve using the Simplex Method The Cut-Right Knife Company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef's knife. The Regular Set consists of 2 utility knives and 1 chef's knife and 1 bread knife. The Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 bread knife. Their profit is $30 on a Basic Set, $40 on a Regular Set, and $60 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 bread knives. Assuming all sets are sold, how many of set should be sold to maximize the profit. What is the maximum profit? O let x, = # basic sets (4 ) X, X2 X 3 S, S2 S3 7 X 2 = # Regular Set 266.7 2 2 3 O C X3 = # Deluxe 800 too 400 Basic Regular Deluxe 200 O 200 X ; * 2 - 30 -40 -60 O O O utility 2 2 3 Chef = 600 1 = 400 bread O - 3 R3+ RI -> RI = 200 - R3+ R2 - RZ ( work attached ) profit 30 40 MAX 6ORZ + R4-> R4 2 Maximize 30 x , + 40 X2+ 60 *3 S, S2 S 3 such that 100 2 o -3 200 2 x1 + 2 x2 + 3X 3 - 800 1 200 * + X 2 + X 3 = 400 X O 200 -30 40 $12,00 0 X2+ X3 = 260 for Xi, Xz , X3 zo - RI+2R2-> R2 ( work attached) 15 RI + RX -> R4 3 ) XI X2 X 3 SI S2 53 Z 2x , + 2 x2+ 3x3+ S1 = 800 + 1 a 200 XI + X2 + X3 + Sy = 400 O -I 2. D 200 X2 +x3+ 53 = 200 1 O O 20 0 -30 * - 40 *2 -60 *3+2=0 5 15 15 15000 2x 1 = 200 X3= 200 X1 2100 52= 100 Maximum = $15,000 X,= 100 252 = 200 X 2= 0 S,= 0 52= 100 X 3 = 200 100 basic sets 2 = 15000 o regular sets 4.2 HWK, Day 2 pg 186-187 #11, 12, 21, 22a, 200 deluxe sets\f3. A manufacturer produces three types of plastic fixtures. The time required for molding, trimming, and packaging is given in table (times given are in hours per dozen fixtures) Total time Process Type A Type B Type C available Molding 2 N Q 12,000 Trimming 4,600 WIN WIN NIH WIN Packaging 2,400 Profit RM 11 RM 16 RM 15 How many dozen of each type of fixture should be produced to obtain a maximum profit