1.
BB 1.3
a)
The production manager wants to minimize total costs
TC = P
E
*E + P
L
*L
.
b)
The constraint is to produce
Q =
200 units, so the manager must choose
E
and
L
so that
EL
= 200.
c)
The endogenous variables are
E
and
L
, because those are the variables
over which the production manager has control.
By contrast, the
exogenous variables are
Q
,
P
E
, and
P
L
because the production manager
has no control over their values and must take them as given.
d)
,
min
. .
200
E L
E
L
P E
P L
s t
EL
+
=
e)
The Langrange is
(
200)
E
L
P E
P L
EL
λ
+
+
−
.
FOC wrt. E:
1
0
2
E
L
P
E
λ
+
=
;
FOC wrt. L:
1
0
2
L
E
P
L
λ
+
=
.
From the above two equations, we get
E
L
P
L
P
E
=
or
2
E
L
=
. Then by the
constraint
EL
= 200 we have L=100
2
and E=200
2
.
.
2.
BB 1.13
a)
The objective function is the number of new SUVs sold, which we can
denote by
Q
(
F, G
).
b)
The constraint is that total spending must be less than or equal to
$2million, or
TS
≤
$2 million.

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