4x + 4y </= 600
x + 6y </= 480
x,y >/= 0
define a feasible region, and the objective to be maximised is
O(x,y)=100x + 150y
Now the for a linear program the objective achives its maximum at a vertex of the feasible region unless it is parallel to an edge when it achives its maximum all along the edge.
So here we find all the vertices of the feasible region and evaluate the objevtive at them and the one where the objective is largest is the optimal point (if two of them both give the maximum of the objective then all the points along the edge of the feasible region conecting those vertices are optima).