A company needs 300 items per year. Production costs are $70 to prepare for a production run and $6 for each item produced. Inventory costs are $0.75 per item per year. Find the number of items that should be produced in each run so that the total costs of production and storage are minimized.

Question

A company needs 300 items per year. Production costs are $70 to prepare for a production run and $6 for each item produced. Inventory costs are $0.75 per item per year. Find the number of items that should be produced in each run so that the total costs of production and storage are minimized. ​​

Quizplus · Accepted Answer

The optimal production quantity is the square root of (2*production cost*annual demand)/inventory cost. In this case, the optimal production quantity is sqrt(2*70*300/0.75) = 237.

A Company Needs 300 Items Per Year