Unformatted text preview: Math 482 HWZ Do four of the ﬁve problems below. Due L;.:j..—. r ' ' I ",l' 1. A farmer has 100 acres of land which he has decided to make part arable
and part grass. Part of the land may also he fallow. He can make an annual proﬁt
of $ 150/ acre from arable land and $ 100/acre from grass. Each year arable land
requires 25 hours work per acre, and grass requires 10 hours work per acre. The
farmer does not want to work more than 2000 hours in any year. How should he
divide his land between arable and grass so as to maximize his annual proﬁt‘.7 2. Solve the LP represented by the tableau below $1$2 173
z
ME—
x20 1 01/2 2 Be careful. Note that am 71$ 0.‘ t
3. Use the simplex method to solve the LP Minimize z = —5$1 — 53:2 — 3333
subject to 1'1 +3532 +533 S 3
—IL‘1 +3.53 S 2
25B} —.’L'2 +2533 S 4
23:1 +3332 —.’E3 3 2
$1, 332, 3U3 2 0 4. Solve the LP
Minimize z = :21 + 3332 + 3333 + 3134 subject to 2x1 +5932 —3x3 +x4 = 2,
3:51 ——2:132 +6323 —a:4 = 1, 7331 +5352 +364 5, 0 IV  321, 272,333 (:54 is unrestricted in sign). Note that this problem is not in the standard form. 5. Prove that if a variable ms was moved out of the basis of a linear program at
some step of the simplex method, then at the next step it will NOT be moved into
the basis again. ...
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 Spring '08
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