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The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery operates five days a week, 52 weeks a year, and can produce cakes at a rate of 132 cakes per day.

- The bakery sets up the cake production operation and produces until a predetermined number (Q) has been produced.
- When not producing cakes, the bakery uses its personnel and facilities for producing other bakery items.
- The setup cost for a production run of cakes is $800.
- The cost of holding frozen cakes in storage is $12 per cake per year.
- The annual demand for frozen cakes, which is constant over time, is 7,400 cakes.

Determine the optimal production quantity (Q) to minimize the total cost of setup and holding.

Answer :

The Ambrosia Bakery produces 132 cakes per day for 260 days a year (52 weeks x 5 days). The setup cost for a production run is $800. The holding cost for frozen cakes is $12 per cake per year. The annual demand for frozen cakes is 7,400 cakes.

To calculate the number of cakes produced per year, we multiply the production rate per day (132 cakes) by the number of operational days in a year (260 days). This gives us a total of 34,320 cakes produced annually.

The setup cost is incurred each time the bakery initiates a production run. So, if the predetermined number of cakes to be produced (Q) is less than or equal to 34,320, the setup cost of $800 will be incurred.

The holding cost is the cost of storing frozen cakes. Since the holding cost is given as $12 per cake per year, we multiply it by the total annual demand of 7,400 cakes. This gives us a holding cost of $88,800 per year.

In summary, the bakery produces 34,320 cakes per year, incurs a setup cost of $800 if the production run is less than or equal to this quantity, and faces a holding cost of $88,800 per year for storing the frozen cakes.

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