Question

Maximize 30x +20y

2x+y <80(Machine 1)

X+3y <80 (Machine 2)

X,y > 0 (non negativity condition)

Calculate optimal product mix.

One of the managers examined your LP model and noted that you did not take into account the requirement that a total of at least 60 products will be produced each week.Would this new constraint change the optimal product mix ? If yes, how would the optimal solution change? If not, explain why the new constraint does not change the optimal product mix.

Answer 1

The points of optimality are ( 0.26.6) ( 32.16) and (40,0)

Value of objective function

at (0.26.6) or (0,26) = 0+26x20 =520

at (32,16) = 960+320 =1280

at (40,0) =800

The optimum result is obtained at ( 32,16)

The introduction of a new constraint x+y<60 does not make any difference as the existing constraints are already within the region bound by this new constraint, as can be seen in the graph. Hence ethe change will nto make any difference in the optimal product mix.