a) all points on the line segment
b) all points on the yellow side excluding the line segment
c) all points on the yellow side including the line segment
d) all points on the blue side excluding the line segment
e) all points on the blue side including the line
segment
a) all points on the yellow side excluding the line
b) above the line (excludes the line)
c) part b
above
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Questions?]
Min .8A + .6B
st:
12A + 3B >= 30
4A + 8B >= 24
A, B >= 0
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Max 2x1 + 3x2st:
3x1 + x2 >= 6
x1 + 7x2 >= 7
x1 + x2 <= 4
x1, x2 >= 0
c) three extreme points:
point A : x1 = 1; x2 = 3
point B : x1 = 7/4; x2 = 3/4
point C : x1 = 3 1/2; x2 = 1/2
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max 6x1 + 2x2st:
(1) 2x1 + 4x2 <=20
(2) 3x1 + 5x2 >= 15
(3) x1 >= 3
x2 >= 0
b) slack/surplus variables:
s1 = 0 (slack)
s2 = 15 (surplus)
s3 = 7 (surplus)
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- b) Constraint E + F <= 290 is redundant as it has no part in forming the feasible region.
-
c) From the graph we see that for the constraint to become active
it must pass through the point of optimality, or point
(118.4,152.6) must lie on the constraint. This happens when the
rhs is = 118.4 + 152.6 or 271.2. The constraint
E + F <= 271.2
passes through the point of optimality. -
d) For this to happen we want the coefficient of E, say c, be
such that c*E + 1*F = 290 passes through the optimal point. Thus
c*(118.4) + 1*(152.6) = 290. Solving for c, we find c = 1.16. The
constraint:
1.16E + F <=290
passes through the optimal point. -
e) Notice from the graph that as the objective coeficient of E
is increases each contour becomes steeper. If the
increase is sufficient, the contour will become tangent to the
feasible region along the line segment II and III. When this
happens objective value will be the same at both of these points
--the coordinates at point III are (150,100). If the objective
function is denoted by c*E + 1000*F, we want
c*(150) + 1000*(100) = c*(118.4) + 1000*(152.6)
solving this for c, we find c = 1667. Therefore if the objective function is
1667E +1000F then both corners II and III (and any point on the line segment) would be optimal.