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Suggested Solution to Midterm 1
1. (Your optimal solution is graded according to your feasible region and isoproﬁt line. Your
z
*
and binding constraints are graded according to your optimal solution. Your Part (e) is
graded according to your feasible region.)
(a) See the graph below.
(b) See the graph below.
x
x
1
2
(1)
(2)
(3)
isoprofit
improving
direction
(c) The problem is unbounded (no matter how far you push your isoproﬁt line, you can still
ﬁnd a feasible point on the isoproﬁt line). Therefore,
z
*
= (
∞
). If you claim (

1
3
,

14
3
)
as your optimal solution, you should answer
z
*
=
25
3
here.
(d) Since there is no optimal solution, there is no binding constraint “at the optimal solu
tion”. If you claim (

1
3
,

14
3
) as your optimal solution, you should answer constraints
(1) and (2) here.
(e)
i. Multiple solutions. Please note this is “min” rather than “max”.
ii. Unbounded.
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 Spring '07
 Zhang

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