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Unformatted text preview: ¢_\ 1 Test 31
Name Qﬂ 2’ U h (2 (I . 3 _— "I751 “ ‘  R5
Simplex Basics Exam (Mn :k, ”W ) lE 280
Spring 2004 NWDT This test is to be completed inclass, with no notes. Calculators are allowed, but if a
particular solution method is required, it must be used to receive full credit for the
problem. The entire class period is allowed for the exam, please do your work that you want graded on the provided paper. Turn off your cellphone. 1. (15) Consider the following problem. max 2 = 2x1 + 3x2 s.t.xl +3ch2 +51 :6 3x1+2x2 +32 =6 x],x2,sﬁ,5220 It has 4 variables and 2 constraints so it has 6 basic solutions. Fill in the following table in order to complete the following steps:
3. Identify those 6 basic solutions by identifying the nonbasic variables and basic variables. g?
b. Tell me the values of all variables at all solutions (including the nonbasic
variables). 51;". .3." 0. Tell me which basic solutions are feasible. 2 Basic
Solution NBV BV Feasible? d. How many different physical points do these basic solutions correspond to? That is, how many corner points (feasible or infeasible) would you have if you graphed this with x1 and x2 as the axes? (0 II 5 . . A Test 3—1
Name SD] (.1 hgﬂ‘ S 2. (10)Consider the following simplex tableau for a maximization problem. a. What should the BV column contain? Write your answer in the tableau shown
abOVe Sta; axiom/e 3 b. What values do the basic variables in row 1 and 2 have?
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c. What is the value of the objective function at this point?
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d. is the problem solved optimally? Yes 1 w b/C “HUME ’15 61» If yes, list the value of all of the variables: _
if no, what are the entering variable and the exiting variable, if any? "1: Wflfg l/CU‘ix'GLiole : 3;
“mint 050. no Qxihig Var gable; WW6
WI 062 11.6) Vet/(JED) mites. ,"  . Test 3—1
'1 Name SEEHZZZQZZS fl: 3. (25) Solve this problem using the simplex method. Be sure to show your work.  If strongly recommend making a notation on your page as to what eros you use to
move from one iteration to the next. If the problem has one or more optimal
solution, indicate this fact and provide the values of the solution for one optimal point. max 2 a 2x] — 4x2 + 51c3 — 6x4 s.t. x] +4352 —2x3 +8.7:4 S 2
—)c1 +2x2 +31:3 +4Jc4 SI Jc1,3c2,.7c3,x4 20 d) ?p+5 Sir 1w
2p+5 ﬁr" ﬂy/eﬁla/jégw 3 PB by W515i! 127%? (Wm!
wag awe/051m 5P+J no+ awn/{1 W [Myra/Hi MW 31 P73 \—..u—— W551! Lo W13; WU‘ ' 3/9“}; ...
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 Spring '08
 Kurz

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