Bonus problem for Friday, 3/1. 5 bonus points on Test 2. To receive bonus credit you must HAND IN
the problems written up by the beginning of class on Friday.
In class, we have been working with the following LP.
max
10x1 + 8x2 + 4x3 + x4
(value)
s.t.
7x1 + 5x2 + 5x3 + 2x4 ≤ 18
(knapsack capacity)
x1 , x2 , x3 , x4 ≥ 0
Recall that we have calculated

0
18/5


=

 0 

x(3)
0
and

1
−7/5


=

 0 
b (1)
d

0
−1
 
= 
1
b (3)
d

0
−2/5


=

 0 



b (4)
d
0
0
Let y be a given vector such that y1 , y2 , y3 , y4 ≥ 0 and
7y1 + 5y2 + 5y3 + 2y4 < 18
To receive bonus credit:
(1) Determine w1 , w2 , w3 , and w4 such that
b (1) + w3 d
b (3) + w4 d
b (4) .
y = w2 x(3) + w1 d
(2) Prove your answer is correct.
You must show all work.
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