Question

Lagrange problem: given the solutions: x=11.587 y=2.34 lamda1=0.32 lamda2=0 given the constraints: 4x+9y =< 72 x+3y =< 21 . Would optimizer of problem want to have more of resource associated with first constraint, or more with the second?

Answer 1

in lagrange method , lambda is the shadow price of that constraint . means the effect of that constraint on the objective function.. so here in our problem , lambda 2 is 0 . this means that 2nd constraints change no effect on optimization.. and lambda 1 = 0.32 .. so it means 1 unit change in 1st constraint make 0.32 unit change in optimizaton function..

so we want to have more of resource associated with 1st constraint ..  ......

any query in this then comment below .. i will explain you