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m [N’I’E a 2002. HN’Z— [NR/“Um 4.4.1: Find the rank of the following set of vectors 1", a basis for this
set, representation of each nonbasic vector in terms of this basis; and
determine for each nonbasic vector which basic vectors it can replace
to lead to another basis: (i): I‘ = {(1,0,—1,2, 1), (—1,1,2, —1,0),
(3, —1, —4,5, 2), (1,1,1,0, 2), (1,2,2, 1,3)} (ii): I‘ = {(1,1, —1,2,1),
(2,—1,2,1,2), (4,1,0,5,4), (0,0,1,0,0), (7, 1,2,8, 7)}. \ L933 (I) FWquswaR/nchﬂaamhg} WQMdefn/W Vow Com Wire QJ/rmzrbgtmti,
QWWO‘W dlowgoﬂmw 2 forum/“Mecca 1. __12 Aforestry company has four, sites on Which they ' grow trees. They, ar =5 onsidering four species 'ot trees the pines spruées; Walnuts, and other 3" hardwoods Data on. the problem are given .. 2'. snow; How much,area s_"houid the company
devote _th the grouting of various species in the Expected Annual, Revenue from Species
.(rnoney units per ka) _  .,  .Area Available
its... _ 'atS_ite'_ _ "'
" {Kai ....Spruée Walnut .. Hardwood . . . " "(Minimal requ_ir__ed _
xpected annual yield . m3) medium, and small. which yield a net unit profit :3 1.14 A product can be made in three sizes, large,
of $12, 10, and 9, respectively. The company Manufacturing this product requires cooling has three centers where this product can be
manufactured and these centers have a
capacity of turning out 550, 750, and 27‘s units of
the product per day, respectively, regardless of
the size or combination of sizes involved. ewes)“ ,
one 6" W“ tn water and each unit of large, medium, and
small sizes produced require 21. 17, and 9
gallons of water, respectively. The centers 1, 2,
and 3 have 10,000, 7000. and 4200 gallons of
cooling water available per day, respectively.
Market studies indicate that there is a market
for 700, 900, and 450 units of the large, medium,
and small sizes, respectively, per day. By
company policy, the traction (scheduled
production)l(center's capacity) must be the
same at all the centers. How many units of each
of the sizes should be produced at the various
centers in order to maximize the profit? ...
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