● Suppose
c i, j = cost of producing one type i hat at factory j
for i ∈ H and j ∈ F
● If we produce x i, j hats of type i at factory j (for i ∈ H and j ∈ F), then the total cost is
Problem �. Let M = {�, �, �} and N = {�, �, �, �}. Write the following as compactly as possible using
summation notation and “for” statements.
Let y� = amount of product � produced
y� = amount of product � produced
of
y� = amount of product � produced
y� = amount of product � produced
}
let
yiamponinucotspndygtiien
first
a�,� y� + a�,� y� + a�,� y� + a�,� y� = b�
a�,� y� + a�,� y� + a�,� y� + a�,� y� = b�
(
@
}
a�,� y� + a�,� y� + a�,� y� + a�,� y� = b�
§µaijyj=
bi
for
iem
Letyiamountofproductiproducedforie
Explanation
-
We
can
@
rewrite
using
for statement
a
.
|
To rewrite
a
@
the 3
equations
rewrite
|§AijYj=biforieM
statement
for
in
Then
,
we
can
we
,
,
L
,
+
rewrite
Ai
can
,
the
ifz
Ai
+
,
}
Is
+
Ain ye,
in
=
be
I
for
line
it
left hand sides of these equations using
-
�
using
M
a
{
: