Question

Maximize objective function P=3x+4y

subject to: x + y ≤ 7 x ≥ 0

x+4y ≤ 16 y ≥ 0

Attach image from graphing calculator or draw your own graph, if desired – must show feasible region and identify critical (corner) points to receive full credit!

Answer 1

The given constraints are x + y ≤ 7 or, y ≤ -x+ 7 …(1), x+4y ≤ 16 or, y ≤ -(x/4)+4…(2) , x ≥ 0… (3) and y ≥ 0… (4).

A graph of the lines y = -x+ 7 ( in red) and y = -(x/4)+4 ( in blue) is attached. The feasible region is part of the 1^st quadrant ( as x ≥ 0 and y ≥ 0) on or below the red line and on and below the blue line. The 2 lines intersect at the point (4,3) where all the constraints are satisfied. Hence the maximum value of P(x,y) = 3x+4y, subject to the given constraints is 3*4+4*3 = 12+12 = 24.