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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 50 "Graphical solution meth
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{TEXT 300 6 "type 1" }{TEXT -1 10 " requires " }{TEXT 301 11 "2 hrs la
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{TEXT -1 16 "and contributes " }{TEXT 303 6 "2.25 $" }{TEXT -1 14 " to
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{TEXT 305 10 "1 hr labor" }{TEXT -1 2 ", " }{TEXT 306 12 "2 ozs metal \+
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{PARA 0 "" 0 "" {TEXT -1 16 "The company has " }{TEXT 308 14 "4000 hrs
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10 " per week." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 29 "The problem is formulated as:" }}{PARA 0 "" 0 "" {TEXT 
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{TEXT -1 47 "                                               " }{TEXT 
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 >=  0" }}{PARA 0 "" 0 "" {TEXT -1 7 " where " }{TEXT 260 1 "x" }
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Plot this line for " }{TEXT 282 5 
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STICKSG6$FeimFfjl-%%VIEWG6$;FcjlFdim;FcjlFejl" 1 2 0 1 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "
The  " }{TEXT 290 17 "optimal solution " }{TEXT -1 12 " is at the  " }
{TEXT 292 12 "intersection" }{TEXT -1 6 "  of  " }{TEXT 293 12 "labor(
x,y,4)" }{TEXT -1 7 "  and  " }{TEXT 294 12 "metal(x,y,5)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "\{labor(x,y,4),metal(x,y,5)\};" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,(%\"xG\"\"#%\"yG\"\"\"!\"%F(,(F%F(F
'F&!\"&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "solve(\{labor(
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%\"xG\"\"\"/%\"yG\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " }
{TEXT 295 7 " value " }{TEXT -1 9 " of the  " }{TEXT 296 18 "objective
 function" }{TEXT -1 13 "  at a point " }{TEXT 297 6 " (a,b)" }{TEXT 
-1 4 "  is" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "obj:=proc(a,b
) subs(x=a,subs(y=b,solve(profit(x,y,z),z))); end;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$objGR6$%\"aG%\"bG6\"F)F)-%%subsG6$/%\"xG9$-F+6$/%
\"yG9%-%&solveG6$-%'profitG6%F.F3%\"zGF;F)F)F)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "obj(1,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"++++]u!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "To determine the \+
" }{TEXT 298 22 "contribution to profit" }{TEXT -1 7 " of an " }{TEXT 
299 24 "additional hour of labor" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "solve(\{labor(x,y,4.001),metal(x,y,5)\},\{x,y\});" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"yG$\"+nmm**>!\"*/%\"xG$\"+nmm+5F
(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "obj(1.000666667,1.9996
66667);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+NLj]u!\"*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "obj(1.000666667,1.999666667)-obj(1,
2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'NLj!\"*" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 45 "solve(\{labor(x,y,4),metal(x,y,5.001)\},\{x
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\"+nmm'***!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "obj(.99966
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{VIEWOPTS 1 1 0 1 1 1803 }