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andout Assignment $4$: Inventory Management

$1-$ The Nougat Bakery makes cakes for freezing and subsequent sale. The bakery, which operates $6$ days a week, $50$ weeks a year, can produce cakes at the rate of $100$ 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 $$600.$ The cost of holding frozen cakes in storage is $$10$ per cake per year. The annual demand for frozen cakes, which is constant over time, is $6000$ cakes. Determine the optimal production run quantity, total annual inventory costs, optimal number of production runs per year, optimal cycle time $($time between run starts$),$ run length in working days.