10/9 More optimization

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10/9 More optimization Test 2 is scheduled
for next Monday, October 16 5-7pm Come to this
room, FB 200, to take the test. This is a room
change from what was previously announced.
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Example to show an unbounded problem can have a
maximum Maximize P -2x y, where x,ygt 0, y
gt x, and yltx2
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• The simplex algorithm
• Find the most negative entry in the bottom row.
  This
• determines the pivot column. Bringing this
  variable
• into solution increases the objective the
  quickest.
• Note If there are no negative entries you
  are already
• at the maximum value. Stop.
• Calculate all the positive ratios in the pivot
  column. Find the smallest one. This determines
  the pivot row.Note if there are no positive
  ratios in the column,the problem is unbounded
  and has no maximum. Stop.
• Perform a pivot operation using the entry in the
  pivot row and pivot column.
• Repeat steps 1 thru 3 until you reach the
  maximumor discover the objective has no maximum.

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Final tableau with maximum example x y s
t P rhs
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Final tableau with no maximum example x
y s t P rhs -1 -1 1 0 0 10
2 -1 0 1 0 20 -1 -2 0 0 1 0
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What kind of tableau is this? x y s t
r P rhs -1 -1 1 0 0 0 -10 1
1 0 1 0 0 40 -1 1 0 0 1 0 20
-3 -2 0 0 0 1 0
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Asset allocation p. 240 36 200,000 to invest
x in growth, y in balanced, z in income
rate of return 12 10
6 risk factor .1
.06 .02 Wants at least 50
in income at least 25 in balancedwith average
risk factor not to exceed .06 Find an optimum
portfolio (x,y,z)
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Initial tableau x,y,z nonbasic (decision)
vars s,t,r basic
(slack) vars (1 for each constraint)
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