Problem 13.6 The Ambrosia Bakery makes cakes for freezing and subsequent sale. T
ID: 375163 • Letter: P
Question
Problem 13.6 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 124 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 or producing other bakery items. The setup cost or a production run of cakes sS500.The cost of holding frozen cakes in storag s·2 er cake per year. The annual demand for frozen cakes, which is constant over time, is 6,200 cakes. (a) Determine the optimal production run quantity (Q). (Round answer to 2 decimal places, e.g. 52.75.) Optimal production run quantity Click if you would like to Show Work for this question: Open Show WorkExplanation / Answer
Annual demand(D) = 6200 cakes
Number of days in a year = 52 weeks x 5 days = 260 days
Demand rate(d) = D/Number of days in a year = 6200/260 = 23.85 cakes
Production rate(p) = 124 cakes per day
Setup cost(S) = $500
Holding cost(H) = $12 per cake per year
Optimal production run quantity = Sqrt of [ (2DS) / {H[1-(d/p)]} ]
= Sqrt of [(2X6200X500) / {12[1-(23.85/124)]} ]
= Sqrt of [(6200000) / (12 X0.81) ]
= Sqrt of (6200000 / 9.72)
= 798.66 cakes