units for component 1, 4000 units for component 2, and 3500 units for component
3. The objective is to minimize the total manufacturing and purchasing costs.
b)
What is the optimal solution? How many units of each component should be
manufactured and how many units should be purchased?
c)
Which departments are limiting Benson’s manufacturing quantities? Use the dual
price to determine the value of an extra hour in each of these departments.
d)
Suppose that Benson had to obtain one additional unit of component 2. Discuss
what the dual price for the component 2 constraint tells us about the cost to obtain
the additional unit.
Solution
3
3
≥
0

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b.
Source
Component
1
Component
2
Component 3
Manufacture
2000
4000
1400
Purchase
4000
0
2100
Total Cost: $73,550
c.
Since the slack is 0 in the production and the testing & packaging
departments, these department are limiting Benson's manufacturing
quantities.
Dual prices information:
Production
$0.906/minute x 60 minutes = $54.36 per hour
Testing/Packaging
$0.125/minute x 60 minutes = $ 7.50
per hour
d. The dual price is -$7.969.
this tells us that the value of the optimal solution
will worsen (the cost will increase) by $7.969 for an additional unit of
component 2.
Note that although component 2 has a purchase cost per unit
of $8.80, it would only cost Benson $7.969 to obtain an additional unit of
component 2.

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