Business math?

  1. A supermarket bakery must decide how many birthday cakes to prepare for the upcoming weekend. Cakes cost $66 each to make, and they sell for $94 each. Unsold cakes are sold at $33 on Monday, and typically all the remaining cakes are sold at that price on Monday. Demand is normally distributed with the mean of 144 and standard deviation of  28.8. Determine the followings:
    Cost of Shortage (Cs):

Cost of excess?

What is the optimal service level?

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What is the corresponding Z value?

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What is the optimal number of birthday cakes to make for the weekend? 

  1. A large bakery makes cakes for freezing and subsequent sale. The bakery can produce cakes at the rate of 1875 cakes per day. The bakery sets up the cake-production operation and produces until a predetermined number (Q) have 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 $100. The cost of holding frozen cakes in storage is $9 per cake per year. The annual demand for frozen cakes, which is constant over time, is 54600 cakes. Assume 364 days a year and 52 weeks a year.


What is the “daily” demand rate? 


How many frozen cakes to produce in a production cycle? (keep two decimal places)

How many cakes are in the freezers when the bakery stops the production in a given production cycle? (keep two decimal places)

How many “days” is the production cycle? 

How many “days” in each production cycle the bakery produces cakes to freeze?

How many “days” in each production cycle the bakery is not producing cakes and can use its personnel and facilities for producing “other” bakery items? 


How much is the total annual inventory related costs?

3) A bakery buys sugar from a big distributor to use in baking cakes. Typically, they use 3675 bags of sugar in a year. The price of sugar is typically $14 per bag. The cost to the bakery for placing an order is $25, and the annual carrying cost is $20 per bag. The distributor has offered the bakery the following volume discount schedule:
 

Order SizeDiscount rate on the original price
1–4490 percent
450–7995 percent
more than 80010 percent


 
We are trying to find how many bags of sugar should the store order, whenever they place a new order of sugar.Assume 364 days a year and 52 weeks a year.


IMPORTANT: Note, the discounts off of original price are reported. You need to calculate the actual prices.


Keep two decimal places in your calculations.If we ignore the discounts, how many bags of sugar should we order? 

Fill in the blanks:
 

Order QuantityUnit Price to PayTotal Annual Inventory Related Cost
Quantity from EOQ model
Enough to get 5 percent discount
Enough to get 10 percent discount

Based on this quantity discount information, how may bags of sugar should the store order? 

How often (in “days”) should the bakery order?

  1. A bakery buys sugar from a big distributor to use in baking cakes. Typically, they use 30 pounds of sugar in a day. But depending on the day, they may use a little bit less or more. It is estimated that the standard deviation of demand for sugar is 3 lbs per day. It takes 4 days from the time the bakery orders sugar until the distributor delivers the sugar. The manager wants to have a service level of 0.8.

Determine each of the following, assuming that demand is distributed normally.


Z value for the intended service level


The safety stock that will provide the intended service level: 


The ROP that will provide the intended service level :

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