2 If the objective functio ? n is ?Q = x y ? and you know? tha? t? + ?y= 10, write the objective function first in ter ? ms of ?x and then in ter? ms of ?y.

Solution Step 1: Given objective function isc And constraints x+y=10 Step 2: (a) We write the objective function in terms of x first We have the constraints x+y=10 y = 10x Step 3: Substituting for y the objective function becomes Q=x y2 Q=x (10x) Q=10x x 3 ;0 x 10 Which is the function of single variable x.with Q(0)=Q(10)=0