Wegmans Bakery produces cheesecake for sale. The bakery, which operates $5$ days per week and $52$ weeks per year, can produce $40$ 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 cheesecake is $\$250$ . The holding cost is $\$5$ per year. The annual demand for cheesecake is constant during the year and is equal to $3900$ . Determine the following: Round answers to the 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).

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Q. Wegmans Bakery produces cheesecake for sale. The bakery, which operates

5

days per week and

52

weeks per year, can produce

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 cheesecake is

\$250

. The holding cost is

\$5

per year. The annual demand for cheesecake is constant during the year and is equal to

3900

. Determine the following: Round answers to the 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).

Calculate total annual production: Calculate the bakery's total annual production capacity. $\newline$ Total annual production = $40$ cakes/day $*$ $5$ days/week $*$ $52$ weeks/year $\newline$ Total annual production = $40 * 5 * 52$ $\newline$ Total annual production = $10400$ cakes/year
Use EPQ model for optimal quantity: Use the Economic Production Quantity (EPQ) model to find the optimal production run quantity $Q$ . $\newline$ EPQ formula: $Q = \sqrt{(2 \cdot D \cdot S) / H} \cdot \sqrt{P / (P - D)}$ $\newline$ Where $D =$ annual demand, $S =$ setup cost, $H =$ holding cost per unit per year, $P =$ production rate. $\newline$ First, calculate $P$ , the production rate. $\newline$ P = Total annual production / Total working days in a year $\newline$ P = $10400$ cakes/year / ( $5$ days/week $\cdot 52$ weeks/year) $\newline$ P = $Q = \sqrt{(2 \cdot D \cdot S) / H} \cdot \sqrt{P / (P - D)}$ $0$ $\newline$ P = $Q = \sqrt{(2 \cdot D \cdot S) / H} \cdot \sqrt{P / (P - D)}$ $1$ cakes/day
Plug values into EPQ formula: Now, plug in the values into the EPQ formula. $\newline$ $D = 3900$ cakes/year, $S = \$250$ , $H = \$5/cake/year$ , $P = 40$ cakes/day. $\newline$ $Q = \sqrt{(2 \times 3900 \times 250) / 5} \times \sqrt{40 / (40 - 3900/260)}$ $\newline$ $Q = \sqrt{(2 \times 3900 \times 250) / 5} \times \sqrt{40 / (40 - 15)}$ $\newline$ $Q = \sqrt{1950000 / 5} \times \sqrt{40 / 25}$ $\newline$ $Q = \sqrt{390000} \times \sqrt{1.6}$ $\newline$ $Q = 624.5 \times 1.2649$ $\newline$ $Q = 790.14$ $\newline$ Round $S = \$250$ $0$ to the nearest whole number. $\newline$ $S = \$250$ $1$ cakes
Calculate total annual inventory cost: Calculate the total annual inventory cost $AHC + AOC$ . $AHC$ (Annual Holding Cost) = $\frac{Q}{2} \times H$ $AOC$ (Annual Ordering Cost) = $\frac{D}{Q} \times S$ First, calculate $AHC$ . $AHC = \frac{790}{2} \times 5$ $AHC = 395 \times 5$ $AHC = \$(1975)$
Determine production runs per year: Now, calculate AOC. $\newline$ $AOC = \frac{3900}{790} \times 250$ $\newline$ $AOC = 4.9367 \times 250$ $\newline$ $AOC = \$(1234.18)$ $\newline$ Round AOC to the nearest whole number. $\newline$ $AOC \approx \$(1234)$
Calculate run length in days: Add $AHC$ and $AOC$ to get the total annual inventory cost. $\newline$ Total annual inventory cost = $AHC + AOC$ $\newline$ Total annual inventory cost = $1975 + 1234$ $\newline$ Total annual inventory cost = $\$3209$
Calculate run length in days: Add $AHC$ and $AOC$ to get the total annual inventory cost. $\newline$ Total annual inventory cost = $AHC + AOC$ $\newline$ Total annual inventory cost = $1975 + 1234$ $\newline$ Total annual inventory cost = $\$3209$ Determine the optimal number of production runs per year $(N)$ . $\newline$ $N = \frac{D}{Q}$ $\newline$ $N = \frac{3900}{790}$ $\newline$ $N = 4.9367$ $\newline$ Round $N$ to the nearest whole number. $\newline$ $AOC$ $0$ runs/year
Calculate run length in days: Add $AHC$ and $AOC$ to get the total annual inventory cost. $\newline$ Total annual inventory cost = $AHC + AOC$ $\newline$ Total annual inventory cost = $1975 + 1234$ $\newline$ Total annual inventory cost = $\$3209$ Determine the optimal number of production runs per year $(N)$ . $\newline$ $N = \frac{D}{Q}$ $\newline$ $N = \frac{3900}{790}$ $\newline$ $N = 4.9367$ $\newline$ Round $N$ to the nearest whole number. $\newline$ $AOC$ $0$ runs/year Calculate the run length (production run time) in days. $\newline$ Run length = $AOC$ $1$ $\newline$ Run length = $AOC$ $2$ $\newline$ Run length = $AOC$ $3$ days $\newline$ Round run length to the nearest whole number. $\newline$ Run length $AOC$ $4$ days