... 1300 156 3 .83 0
W36 ¥ 280 82 .40 36.52 0 .88 5 16.595 1.570 189 00 1030 15.10 1200 144 3 .81 0
W36 ¥ 260 76.50 36.26 0 .84 0 16.550 1.440 17300 953 15.00 1090 132 3. 780
W36 ¥ 245 72.10 36. 08 0 .80 0 16.510 ... Applications involving
526 INTRODUCTION TO OPTIMUM DESIGN
TABLE 15-3 Some Wide Flange Standard Sections
Section A d t
w
bt
f
I
x
S
x
r
x
I
y
S
y
r
y
W36 ¥ 300 88 .30 36.7...
... trial design point is
(n)
The cost and constraint functions at the new trial design point are calculated as
(o)
ff
g
11
2
1
52 8 0 725 52 8 320 52 8 0 725 15 037
52 8 0 725
52 8
60 0 725
1 0 21 38 ... that has worked fairly well is
388 INTRODUCTION TO OPTIMUM DESIGN
Table 11-1 Simplex Solution Procedure for QP Problem of Example 11.2
X
1
X
2
X
3
X
4
X
5
X
6
X
7
X
8
Y...
...
È
Î
Í
Í
Í
˘
˚
˙
˙
˙
Kx
x
U 10 03
3 1214 9 3642 87 86 1
28 585 0 28 4540 3 300
28 585 0 28 4540 3 300
.
E
∂
()
∂
=
-+
-+
+
È
Î
Í
Í
Í
˘
˚
˙
˙
˙
Kx
U
d
3 1214 03
2 85 85 04
2 85 85 04
.
.
.
E
E
E
∂
∂
=
-
È
Î
Í
Í
Í
˘
˚
˙
˙
˙
∂
∂
=
-
È
Î
Í
Í
Í
˘
˚
˙
˙
˙
g
g
1
1
4 ... 4.3230E-01 9. 083 7E+00
8 CCC 3.53358E-02 1.67623E-02 1.19 085 E-02 5.2692E-02 3 .88 96E-01 9. 082 8E+00
9 CCC 4...
... as
Plotg4=ContourPlot[g4,{x1,-1,25},{x2,-1,25}, ContourShadingÆFalse,
ContoursÆ{0,.35}, ContourStyleÆ{{Thickness[.01]}, {GrayLevel[ .8] ,Thickness[.02]}},
DisplayFunctionÆIdentity];
62 INTRODUCTION TO OPTIMUM ... of a design problem
may not be linear, in which case curves must be plotted to identify the feasible region, and
contours or iso-cost curves must be drawn to identify t...
... 4x
2
subject to x
1
+ 2x
2
£ 5
2x
1
+ x
2
= 4
254 INTRODUCTION TO OPTIMUM DESIGN
232 INTRODUCTION TO OPTIMUM DESIGN
1. For 2x
1
+ x
2
£ 9: y
1
= 1.6 (c¢
3
in column x
3
)
2. For x
1
- 2x
2
£ 2: y
2
= 1 .8 ... 20x
1
- 6x
2
subject to 3x
1
- x
2
≥ 3
Linear Programming Methods for Optimum Design 247
2 28 INTRODUCTION TO OPTIMUM DESIGN
TABLE 6-17 Continued
Third...