Problem
My bother and I are together 20 years old. My brother is 2 years younger than I am. What is our age?
Modeling Steps
How to solve this problem? A first method is “trying”. Just guess! So suppose I am 10, then my brother must be 10 too, but the difference then is 0. If I am 12, my brother must be 8, the difference is 4, it doesn’t match either. Well, in between might work: 11 and 9 is 20 and the difference is 2. Bingo!
Another method is to look systematically through all possibilities…
A systematical way is to use math: Let x and y be positive numbers representing my age and my brother’s age. Then we have
insert y into the first equation: x + x – 2 = 20, so: x = 11.
model exercise1 "A simple modeling example";
variable x "my age";
y "my brother's age";
constraint
A: y = x-2 "y is two less than x";
B: x+y = 20 "x and y together is twenty";
solve;
Write('My age is : %2d' n', x);
Write('My brothr' 's age is: %2d' n', y);
Draw.Scale(10,-10);
Draw.Arrow(0,0,22,0); Draw.Text('x',19,-1);
Draw.Text('11',10.2,-1.5);
Draw.Arrow(0,0,0,22); Draw.Text('y',-1,19);
Draw.Text('9',-1.5,8.5);
{i in 1..20} Draw.Line(i,0,i,0.5);
{i in 1..20} Draw.Line(0,i,0.5,i);
Draw.Line(20.5,-.5,-.5,20.5,3);
Draw.Line(1.5,-.5,14,12,3);
Draw.DefLine('line.dash',18,7);
Draw.Line('#dash',-.5,9,15,9);
Draw.Line('#dash',11,-.5,11,15);
end
References
[1] MatMod. Homepage for Learning Mathematical Modeling : https://matmod.ch.
[2] Hürlimann T. Reference Manual for the LPL Modeling Language, most recent version. https://matmod.ch/lpl/doc/manual.pdf.