Units for component 1 4000 units for component 2 and

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Nature of Mathematics
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Chapter 16 / Exercise 3
Nature of Mathematics
Smith
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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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Nature of Mathematics
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Chapter 16 / Exercise 3
Nature of Mathematics
Smith
Expert Verified
7 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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