Question

Set up the initial simplex tableau that could be used to solve the following problem by the simplex method. The Fancy​ Fashions, an​ independent, local​ boutique, has ​$7000 available each month for advertising. Newspaper ads cost ​$400 ​each, and no more than 40 can run per month. Internet banner ads cost ​$20 ​each, and no more than 50 can run per month. TV ads cost ​$2000 ​each, with a maximum of 10 available each month. Approximately 4000 women will see each newspaper​ ad, 3000 will see each Internet​ banner, and 11 comma 000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize its ad​ exposure? Create Chart: x1_x2_x3_s1_s2_s3_s4_z_ solution

Answer 1

son formulation of Lpp StubI set up the deciso rausibles that a number of newspaper ads 2 number of Internet Bannesade يطلعود ل فهم لا Stap II Objective function we have to maximize the ads exposure Max 2 = 40002, + 300033 + 11000 X3 seep u mliite whe constraints 4002, § 16000 ( Neambabienne) 1 200 s1000 Internet ads 200027 5 20000 ( TV ads undan 400%, + 201, + 20000, < yooo (roudget constraint unds were Solution by simplex Method Invest the problem into canonicas fam by adding stack vauibles, we have Max Z = 4000x4 + 30002, + Ilowo 27+ 0.5, 10:57 0.83 +0-sy Sot 400 2, +S, - 16000 2012 +S2 = 1000 2000x2 + 5z = 20000 4004, +2042 1 2000n + Sy=1000 and ,*2, X3, 3,152,53 Su 30

Iluation 1 Hom/31 001 000 01010 B I Col Xo la, la luz ls, ls, ls, sy Min Ratio S2 S 0 16000 40000 000 10 10000 2010101010 53 10/20000 | 0 l : 2000 | olol 10 20000 =10 S40700040020 (2000) 0101 011010 23:-> 2=0 Zo ooooooo H- -40oo Jooo -Iooc | 0 | | |o| neg. min Entering valable = 23, Deporting Notable = Sy Key Elimout = 2000 All Ry Grew) = Rycold) † 2000 RCnew )= Rold) ky (new) = Rz cold) Rg Cnew) = Ry Cold ) – 2000 Ry (new)

trin Iteration 2 cu 14000 3000) How 0101010 ICB I XB 13, 122, Rz 15, 5, 53 sy Ratio ETT XB/~z si lo 116000 1400 10 lo lilo 100 5210 1000 0 200 10400 omd=50+ 53 | o 13000-400-201 0 00 - - 23 11000 72 Vs You oo Soo97. = 2-38500 ; 2200 H0 11000 10 100 % T 24 41000 -2090 0 0 0 0 12 =350 10000 Yoo neg min Entering variable, At Deporting variable = 5 key element = 20 Ry (new) = R2 cold 25 20 Rnew) = Rold) Ry (new)= Rz (old) 120% new) Ry (new) Rulold) - tor Renew

Iteration 3 G 40003000 News 00100 B |CB|XB|9, 142 143 15, sz Sz|sy Mimino X8/x, To 16000 400 Lolololololo poor - 40 3000 500Lilololololol - 53 10 14000-400 olololi 23 11000 3 (s ol o korg o 172000445-15 2-183000 o 1 zi 12200/3000/11000 10 28% 0 % GT 13-4-1000 000 10 20% 0 % 900 > bregmin Entering variable =*, , departing variable =23 Key Element - Ys Ry (new) = Ry Cold) 25 R, (new) = R, Cold) - 400ky(new) By (new) Recold) Rz (new) = Rz cold) +-400 Rulnew)

Iterations y Co 4ovo 3000 niliwoootorom Sio 10000 Olo 2000 illo 22 3000 5001 lolo 720) olo S210 2000000 2000 ololo 2, Moos 15 0 50 - Vyoo 0 Yos 1/2 =21ovod z 4000 3000 20000 o 140 o llo 940 9000 140 10 since all z-ize rence optimal solution is arrived. 4 5 -50, b=0 O DO May 2= 210000