Problem:

The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery, which operates five days a week, 52 weeks a year, can produce cakes at the rate of 177 cakes per day. The bakery sets up the cake-production operation and produces until a predetermined number (Q) have 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 $651. The cost of holding frozen cakes in storage is $41 per cake per year. The annual demand for frozen cakes, which is constant over time, is 8,340 cakes.

Determine the following:

Question 1) Optimal production run quantity (Q) , (round your answer to the nearest whole number, the tolerance is +/- 1.)

Question 2) Total annual inventory costs $, (round your answer to 2 decimal places, the tolerance is +/- 1.)

Question 3) Optimal number of production runs per year runs, (round your answer to 2 decimal places, the tolerance is +/- 0.1.)

Question 4) Optimal cycle time (time between run starts) days, (round your answer to 2 decimal places, the tolerance is +/- 0.1.)

Question 5) Run length in working days days, (round your answer to 2 decimal places, the tolerance is +/- 0.1.)

Solve the given numerical problem and illustrate step by step calculation.