AMS 341
Spring, 2010
Homework Set # 5 — Solution Notes
#5, 5.1:
a45
a54
x
2
10
C
x
1
10
A
D
B(20
,
10)
(a) The slopes are

1
2
for the first constraint and

2 for the second. To keep the current basis remain optimal, the
slope

c
1
2
of the isoprofit line must satisfy

2
≤ 
c
1
2
≤ 
1
2
. Thus, the profit from type 1 radio
c
1
satisfies 1
≤
c
1
≤
4.
The profit is equal to the price minus the cost of producing one type 1 radio, which is 22. The price of type 1 radio is
between $23 and $26.
(b) Similar to (a), suppose the profit from type 1 radio is fixed, and the profit from type 2 radio is
c
2
the isoprofit line
must satisfy

2
≤ 
3
c
2
≤ 
1
2
. and therefore 1
.
5
≤
c
2
≤
6. The price of type 2 radio is between $21.5 and $26.
(c) At point C, we have
x
1
+ 2
x
2
= 25. As long as laborer 1 work no less than 25 hours per week, the current basis
will remain optimal. Therefore, in this problem the basis is still optimal and the new optimal solution is
z
=
230
3
,x
1
=
70
3
,x
2
=
10
3
.
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 Spring '08
 Arkin,E
 Equals sign, optimal solution, The Shadow, Shadow price, current basis

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