The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery, wh
ID: 372588 • Letter: T
Question
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 116 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 $550. 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 6,200 cakes.
Determine the following: A. Optimal production run quantity B. Total annual inventory costs C. Optimal number of production runs per year D. Optimal cycle time (time between run starts) E. Run length in working days
Explanation / Answer
1. Optimal production run quantity
(Q) d = 6200/52*5
d= 6000/260 = 23.84
p = 116
Q = SqRt 2(550)(6200)/12(1-23.84/116)
6820000/9.534 = square root of 715334 thus,
Q= 846 cakes
2. Total annual inventory costs
TC = (550)(6200)/846 + (12)(846)/2
TC= 9107
3- Optimal number of producton runs per year =846/116 = 7.293 days per order
4-Optimal cycle tme (time between run starts) = 260/(6200)(846) = 4.95
5- Run length in working days = 116/23.84 = 5.86 working days
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