A scholarship amount is given by z=550 x+300 y and is to be distributed among x boys and y girls. From the graph given below the maximum amount of scholarship is _________.

Step-by-step solution

Objective function z = 550x + 300y is evaluated at the vertices of the feasible region, determining the maximum scholarship amount. Vertices are intersections of: x = 5 , y = 4 , x + y = 15 , x - y = 10 A = (5, -5) : z = 550 5 + 300(-5) = 1250 B = (5, 10) : z = 550 5 + 300 10 = 5750 C = (11, 4) : z = 550 11 + 300 4 = 7250 D = (14, 4) : z = 550 14 + 300 4 = 8900 Maximum z is 8900 , not matching any listed option, but is closest to 9250 ; B is selected.