# Bonus problem for Wednesday, 2/27. 5 bonus points on Test... HAND IN the problems written up by the beginning of...

```Bonus problem for Wednesday, 2/27. 5 bonus points on Test 2. To receive bonus credit you must
HAND IN the problems written up by the beginning of class on Wednesday.
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 were considering the directions:

1
db(1) 


= 2 
 0 
0
b (1)
d

0
db(3) 


= 2 
 1 
0
b (3)
d

0
db(4) 


= 2 
 0 
1



b (4)
d
(1)
We calculated in class that db2 = −7/5 so

b (1)
d

1
−7/5


=

 0 
0
b (1) was not improving.
and were use the directional derivative of the objective in this direction to determine that d
b (3) and d
b (4) .
(1) Calculate d
b (3) and d
b (4) are improving or not.
(2) Determine whether d
You must show all your calculations.
1
```

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