(%i2) load ( simplex ) $
load ( "draw" ) $

1 zadatak

(%i10) k : 18 $
l : 14 $
A : 850 $
B : 540 $
m : 25 $
n : 23 $
K : 50 $
maximize_lp ( k · x + l · y , [ x < = A , y < = B , 1 / m · x + 1 / n · y < = K ] ) , nonegative_lp = true ;

\[\operatorname{ }\left[ 20452\operatorname{,}\left[ y=368\operatorname{,}x=850\right] \right] \]

(%i11) wxdraw2d ( grid = true , x_voxel = 60 , y_voxel = 60 , fill_color = green ,
                xtics = { 0 , 100 , 300 , 500 , 700 , 850 } , ytics = { 0 , 200 , 368 , 540 , 600 } ,
                region ( x < = A and y < = B and 1 / m · x + 1 / n · y < = K , x , 0 , A + 100 , y , 0 , B + 100 ) ) ;

\[\operatorname{ }\]

(Graphics)

\[\operatorname{ }\]

(%i12) solve ( 1 / m · x + 1 / n · 540 = K , x ) ;

\[\operatorname{ }\left[ x=\frac{15250}{23}\right] \]

(%i13) solve ( 1 / m · x + 1 / n · 540 = K , x ) , numer ;

\[\]\[rat: replaced -26.52173913043478 by -610/23 = -26.52173913043478 \]\[rat: replaced 0.04 by 1/25 = 0.04 \]\[rat: replaced -26.52173913043478 by -610/23 = -26.52173913043478 \]\[rat: replaced 0.04 by 1/25 = 0.04 \]\[rat: replaced 0.001739130434782609 by 1/575 = 0.001739130434782609 \]\[rat: replaced -663.0434782608695 by -15250/23 = -663.0434782608696\]

\[\operatorname{ }\left[ x=663.0434782608696\right] \]

(%i14) 18 · 15250 / 23 + 14 · 540 , numer ;

\[\operatorname{ }19494.78260869565\]

2 zadatak

(%i23) k : 8 $
l : 11 $
A : 42 $
B : 28 $
PA : 2 $
PB : 3 $
QA : 3 $
QB : 1 $
minimize_lp ( k · p + l · q , [ PA · p + QA · q > = A , PB · p + QB · q > = B ] ) , nonegative_lp = true ;

\[\operatorname{ }\left[ 158\operatorname{,}\left[ q=10\operatorname{,}p=6\right] \right] \]

(%i24) wxdraw2d ( grid = true , x_voxel = 60 , y_voxel = 60 , fill_color = green ,
                xtics = [ 0 , 3 , 30 ] , ytics = { 0 , 5 , 10 , 15 , 20 , 28 , 35 , 40 } ,
                region ( PA · p + QA · q > = A and PB · p + QB · q > = B , p , 0 , 30 , q , 0 , 40 ) ) ;

\[\operatorname{ }\]

(Graphics)

\[\operatorname{ }\]

Created with wxMaxima.