Economic Mathematics Consider the problem of inventory costs and production to satisfy a demand x for a certain product. The data is as follows: Delivery period T = 8 Starting inventory x (0) = 0 Ending inventory x (8) = 144 Inventory cost CI (x (t)) = 7x (t) Production flow cost Cp = 3.5x'2 (t) 1. Write the problem of minimizing total costs over time 2. Check the second order conditions for minimization

Managerial Economics: A Problem Solving Approach
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Chapter7: Economies Of Scale And Scope
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Economic Mathematics

Consider the problem of inventory costs and production to satisfy a demand x for a certain product. The data is as follows:

Delivery period T = 8
Starting inventory x (0) = 0
Ending inventory x (8) = 144
Inventory cost CI (x (t)) = 7x (t)
Production flow cost Cp = 3.5x'2 (t)
1. Write the problem of minimizing total costs over time
2. Check the second order conditions for minimization
3. Raise the Euler equation and the differential equation to solve
4. Find the paths of inventory, production and total costs
5. Graph the inventory and production lanes (use 0.5 increments over time)

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