gvWegmans Bakery produces cheese cake for sale. The bakery which operates 5 days per week and 52 weeks per year can produce cake at the rate of 40 cakes per day. The bakery sets up cake production operation and produces the predetermined quantity Q has been produced. The setup cost for a production run of cheese cake is $250. The holding cost is $5 per year. The annual demand for cheese cake is constant during the year and is equal to 4000. Determine the following: Round answers to nearest whole number. (a) the optimal production run quantity (Q). (b) the total annual inventory cost (AHC AOC). (c) the optimal number of production runs per year. (d) The run length (production run time).

(a) the optimal production run quantity (Q) = 633

(b) the total annual inventory cost (AHC AOC) = $ 3,162.28

(c) the optimal number of production runs per year = 7

(d) The run length (production run time) = 16 days

Explanation:

(a) the optimal production run quantity (Q).

optimal production run quantity = √ (2*Annual Demand*Setup Costs) / Holding Costs

= √ (2*4000*$250) / $5

= 633

(b) the total annual inventory cost (AHC AOC).

total annual inventory cost = Setup Costs + Holding Costs

= 4,000/633*$250+633/2*$5

= $1,579.78+$1,582.50

= $ 3,162.28

(c) the optimal number of production runs per year.

number of production runs per year = Total Demand / optimal production run quantity

= 4,000/633

= 7

(d) The run length (production run time).

production run time = optimal production run quantity / produce

= 633 / 40 cakes

= 16 days