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Answer :
The total annual inventory related costs, including setup cost and cost of holding frozen cakes in storage, amount to $24,710,500.
To determine the daily demand rate, we divide the annual demand for frozen cakes by the number of days in a year. The annual demand is 54600 cakes, and since there are 364 days in a year, the daily demand rate is
54600/364 = 150 cakes per day.
To calculate the number of frozen cakes to produce in a production cycle, we need to find the predetermined number (Q). The bakery produces cakes at a rate of 7500 cakes per day, so the production cycle is Q/7500 days. Since the production cycle is equal to 364 days in a year, we can set up the equation Q/7500 = 364 and solve for
Q. Q = 7500 * 364 = 2736000 cakes.
To find the number of cakes in the freezers when the bakery stops production in a production cycle, we need to calculate the number of cakes produced in a production cycle and subtract the daily demand rate times the number of days in a production cycle. The number of cakes produced in a production cycle is Q = 2736000 cakes. The number of cakes in the freezers is
2736000 - (150 * 364) = 2736000 - 54600 = 2681400 cakes.
The production cycle lasts for 364 days.
During each production cycle, the bakery produces cakes to freeze for 364 days.
The bakery is not producing cakes for the remaining days in a year, which is 364 - 364 = 0 days.
To calculate the total annual inventory related costs, we need to consider the setup cost for a production run and the cost of holding frozen cakes in storage. The setup cost for a production run is $100, and the cost of holding one cake in storage per year is $9. The total number of cakes produced in a year is Q = 2736000 cakes. The total setup cost for a production run is $100. The total cost of holding frozen cakes in storage is
2736000 * $9 = $24,710,400.
The total annual inventory related costs are
$100 + $24,710,400 = $24,710,500.
the daily demand rate for frozen cakes is 150 cakes per day. The bakery needs to produce 2,736,000 cakes in a production cycle, with 2,681,400 cakes in the freezers when production stops. The production cycle lasts for 364 days, during which the bakery produces cakes to freeze. The bakery does not produce cakes for any additional days. The total annual inventory related costs, including setup cost and cost of holding frozen cakes in storage, amount to $24,710,500.
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