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Resource Allocation

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Enpar manufactures a single type of engine part for an automotive manufacturer. It operates two plants, A and B, which have the following production functions: QA = 30 SA - 0.25 SA2 and QB = 40 SB - 0.5 SB2, where QA and QB denote the outputs of engine parts from each plant and SA and SB denote the amounts of steel used in each plant.
Suppose that total steel availability is 40 units. What is the optimal allocation between the two plants?

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Solution Summary

This solution analyzes the optimal allocation of a resource between two plants.

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Given:
QA = 30 SA - 0.25 SA^2
QB = 40 SB - 0.5 SB^2
SA + SB = 40 since the total steel availability is 40 units.
0 <= SA <= 40 and 0 <= SB <=40 since steel consumption ...

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