Question

Solve the following linear programming problem. Restrict x ≥ 0 and y ≥ 0. Minimize g = 38x + 23y subject to the following.
x + y ≥ 100
−x + y ≤ 20
−2x + 3y ≥ 30
(x, y) =
g =

Answer 1

sketch it
lines a , b and c
above line a
below line b
above line c
looking at it, must be to the right of line a, between the intersections of a,b and a,c
it will be one of those intersections because we are looking for the LEAST value of 38x + 23 y
now find those two intersections
a and b
x + y = 100
-x + y = 20
-----------------------
2 y = 120
y = 60
x = 40 so at (40,60 )
and g would be 38 *40 + 23 * 60
now the other point
-2x + 3 y = 30
2x + 2y = 200
==============
5y = 230
y = 46
x = 54 so (54,46)
and g would be 38*54 + 23 * 46

pick the smaller of the g values at those two points