May 2015
Intermediate to advanced
466 pages
10h 33m
English
Content preview from Optimization
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406 Appendix C
13. Let x
ij
= barrels of gasoline of type i used to make fuel of type j
F
j
= barrels of fuel of type j
Prot = Revenue – Cost
The objective function and constraints can be written as
Minimize
( ) ( )
( )
90 100 60 65
70
1 2 11 12 21 22
31 32
F F x x x x
x x
+ − + − +
− + −− +80
41 42
( )x x
subject to
75x
11
+ 85x
21
+ 90x
31
+ 95x
41
− 80F
1
≥ 0
75x
12
+ 85x
22
+ 90x
32
+ 95x
42
− 90F
2
≥ 0
F
1
+ F
2
≥ 6000
0 ≤ (x
11
+ x
12
) ≤ 3000
0 ≤ (x
21
+ x
22
) ≤ 4000
0 ≤ (x
31
+ x
32
) ≤ 5000
0 ≤ (x
41
+ x
42
) ≤ 4000
14. Functions at plots (a) and (d) are convex (see Figure C.4).
15. The Taylor series of a function f(x) at x = a is given by
f a f a
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