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Unformatted text preview: IE 280 Solutions to Sample IP questions 1. Answer the following true / false questions about feasible regions and optimal solutions The graph shows the feasible region
where the variables must be integer
valued. All the integer points are marked
with little dots. Point A is the
intersection of the constraint and x1 2 0 ,
so A is (O, 5.8). Point B is (0,0). Point C
is the intersection of the constraint and x2 2 0, so C is (5.2, 0). Assume the objective function is max xI . Consider the following questions. Point C can be the optimal solution point to this Integer Program. TRUE Q89
me beaming C {3 JEAL t Vt, wit ‘ 7 The point (5, 0) is the optimal solution to the integer; program because it has a @’
TRUE
better objective function value than the point C. I: i \«VCN/t/Ld be, C7ﬂi7MaQ brew/Ad iii i3 iﬂQ‘i ﬂﬁaroimw
O’f MAM WW4“? LUfHﬁ 330m} 3 , 2. Pawtucket University is planning to buy new copier machines for its library. Two models are
available: Model A (highspeed) and Model B (lowerspeed and less expensive). Model A can
handle 20,000 copies a day and costs $6000. Model B can handle 10,000 copies a day but costs only
$4000. At least 6 copiers are required, so that they can be distributed throughout the library. Also,
there must be at least one more high speed copier than low speed copier. Finally, the copiers must be
able to handle at least 75,000 copies per day. The objective is to determine the number of each copier
that should be bought to satisfy these requirements at minimum cost. Formulate an IP to provide this answer. Lei xA X”: r “(add ﬂ ff/l/Lif’FS [Qétéa/M ﬂ l/l/(OCLU A Pfi/Liﬂrg ban/(YLJ‘ 3. Consider the followingIP b 1/ Kmik I mill K4 w.
, B l: ‘7” h > f ,
max 2 = 6x1 +5x2 Ha Mm
s.t.3 +4x $24 A , A \x,
x1 2 x41 X/‘l S XL ‘x‘
xl—ZxZSZ I l I L i
—x1+3xzs3 mel, gXp‘ L/Xg, V;
'  <
xwaZOand‘T—t—ﬂ XVZXZ M l f a. Solve this IP graphically 7 { 2
Write the linear relaxation _ L \ b b 4. Let xi =1 if an option 1' is taken and zero otherwise (i = l, 2, 3, ..., 9, 10). Indicate whether each of the following sets of constraints are correct or not for the following ideas.
21. Option 3 or 4 or both MUST be selected if option 1 or 2 is selected. Potential set of constraints: x3 2 x1 . .
This set Will work NO
x4 2 x2
b. If option 6 is selected, option 7 cannot be selected.
)66 + x7 .<. 1 This constraint will work YES NO $0 i m ‘, Me}
If» aphml 1‘5 CM slaw“;
we ham/Q x. s I
so X52] 90x31! (9 It 31 {5 W w 7 WW1 i 7/
L Liv; Sb XV“ gel/W b: ...
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 Spring '08
 Kurz
 Optimization, optimal solution point, new copier machines, Sample IP questions, high speed copier, low speed copier

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