2-11 Write each of the following as compactly as
possible using summation and "for all" indexed
(a) min 3y3,1 + 3y3,2 + 4y4,1 + 4y4,2
(b) max 1y1,3 + 232,3 + 3y3,3 + 4y4,3
(c) max (1)1,4 + + +
(d) min 81Y1 + 82/22 ... + 8,31
(c) Y1,1 Y1,4 = 51
Y2,1 + Y2,2 + Y2,3 + Y2,4 = 52
Y3,1 + Y3,2 + Y3,3 + Y3,4 = 53
(f) + + a3,1133 + 14,174 = C1
+ + +
+ 02,382 + 03,343 + = C3
2-14 Suppose that the decision variables of a
mathematical programming model are
Kigh st. acres of land plot i allocated
to crop j in year t
where i = 1 47:j= 1 9: t = 1
Use summation and "for all" indexed notation to
write expressions for each of the following systems
of constraints in terms of these decision variables,
and determine how many constraints belong to
(a) The total acres allocated in each year to each
plot i cannot exceed the available acres there
(call it P1).
(b) At least 25% of the total acreage allocated in
each of the first 5 years years should be de-
voted to corn (crop j = 4).
(c) More acres should be devoted to beans (crop
j = 1) in each year and each plot than to any
2-17 Taking the by as variables, and all other sym-
bols as given constants. determine whether each
straint, and briefly explain why.
(a) 3x1 + 2x2 - X17 = 9
= 4x6 + 9x
(c) a/xg + 10x 13 s 100
(d) x4/a + Bx 13 Z 29
2-20 The Forest Service can build a firewatch
tower on any of 8 mountains. Using decision
variables X1 = 1 if a tower is built on mountain
j and = 0 otherwise, write constraint(s) enforc-
ing each of the following requirements.
(a) In all 3 sites will be selected.
(b) Atleast 2 of mountains 1,2,4, and 5 must
(c) A tower should not be built on both
mountains 3 and 8.
(d) A tower can be built on mountain 1 only
if one is built on mountain 4.
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