# Chart Chart1 Solver setup Answer Report Page WID T

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Worksheet: [steel.xls]Sheet1
Report Created: 6/14/99 11:33:00 AM

Target Cell (Max)
Cell                                  Name                                   Original Value     Final Value
\$I\$6    rate at which the cast product comes off the caster (tons/hr.) Value                 0     49.07520012

Cell                                   Name                                  Original Value     Final Value
\$I\$7    thickness of cast product (ins.) Value                                               1     9.999999983
\$I\$8    width of cast product (ins.) Value                                                   0     20.00000001
\$I\$9    length of cast product at the time it solidifies (ft.) Value                         0               60

Constraints
Cell                               Name                                         Cell Value         Formula          Status       Slack
\$C\$26 Aspect ratio <= Max Aspect Ratio                                           2.000000005     \$C\$26<=\$D\$26     Binding                 0
\$C\$30 THICK >= MINTHICK                                                          9.999999983     \$C\$30>=\$D\$30     Not Binding   2.999999983
\$C\$34 Area >= MINAREA                                                            199.9999998     \$C\$34>=\$D\$34     Binding                 0
\$C\$41 LEN <= LENMAX                                                                         60   \$C\$41<=\$D\$41     Binding                 0
\$C\$37 Area <= MAXAREA                                                            199.9999998     \$C\$37<=\$D\$37     Not Binding    50.0000002
A        B           C       D        E       F       G                H             I
1
2                                      Steel Casting Problem
3
4          Variables                     Description                                    Value
5        TPH           rate at which the cast product comes off the caster (tons/hr.)     0
6        THICK         thickness of cast product (ins.)                                   1
7        WID           width of cast product (ins.)                                       0
8        LEN           length of cast product at the time it solidifies (ft.)             0
9        MAXASPR       maximum aspect ratio : WIDTH/THICK                                 2
10       MINTHICK      minimum thickness of cast product (ins.)                           7
11       LENMAX        maximum length before cast product must be solidified (ft.)       60
12       MINAREA       minimum cross-section area of cast product (in^2)                 200
13       MAXAREA       maximum cross-section area of cast product (in^2)                 250
14       k             solidification factor (0.85-1.15)                                  1
15       rho           density of steel                                                 0.284
16
17       Maximize output in tons/hour
18                   TPH = (1.44*rho*k^2)*LEN*WID/THICK
19
20
21
22
23
24
25
26       given the following constraints

Steel
A   B      C      D       E       F          G     H   I
27
28           Aspect ratio <= Max Aspect Ratio
29
30             0       2
31
32           THICK >= MINTHICK
33
34             1       7
35
36           Area >= MINAREA
37
38             0      200
39
40           Area <= MAXAREA
41              0     250
42
43           LEN <= LENMAX
44
45             0       60

Steel
Feasible Set

30

25

20

T=0.5*WID
Thickness

T=200/W
15
T=250/W
T=MinThick
10

5

0
0   5   10   15     20           25   30   35   40

Width
Chart

WID        T=0.5*WID    T=200/W      T=250/W T=MinThick
10            5           20            25      7            MinThick:    7
11          5.5    18.18182     22.72727        7
12            6    16.66667     20.83333        7
13          6.5    15.38462     19.23077        7
14            7    14.28571     17.85714        7
15
16
7.5
8
13.33333
12.5
16.66667
15.625
7
7
Feasible
17          8.5    11.76471     14.70588        7
18            9    11.11111     13.88889        7
19
20
9.5
10
10.52632
10
13.15789
12.5
7
7
30
21         10.5     9.52381     11.90476        7
22           11    9.090909     11.36364        7                25
23         11.5    8.695652     10.86957        7

Thickness
24           12    8.333333     10.41667        7                20
25         12.5            8            10      7
26           13    7.692308     9.615385        7
27         13.5    7.407407     9.259259        7
15
28           14    7.142857     8.928571        7
29         14.5    6.896552      8.62069        7                10
30           15    6.666667     8.333333        7
31
32
15.5
16
6.451613
6.25
8.064516
7.8125
7
7
5
33         16.5    6.060606     7.575758        7
34           17    5.882353     7.352941        7                0
35         17.5    5.714286     7.142857        7
5
Width

Page 5
Chart

Feasible Set

T=0.5*WID
T=200/W
T=250/W
T=MinThick

25            45
Width

Page 6

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