4. (Build your own model for this problem.) Kate’s Cakes is a boutique cake shop in AJ’s Fine Foods supermarket. Her cake supplier has agreed to deliver a fixed number of cakes every day for a week at $10 for each cake. At the end of the week, Kate may change her order for the following week. Kate has kept close track of daily cake demand. The number of cakes sold per day stays about the same over time on average but varies from day to day as shown in the table of value below:

Daily Demand: 1 2 3 4 5 6

Probability: .1 .2 .25 .25 .15 .05

Kate does not believe that being out of stock on a given day influences demand on future days; in particular, she believes that the demand distribution described above will hold on every day, seven days a week (Kate is open every day).

Kate’s initial inventory of cakes is zero. She always keeps any unsold cakes and tries selling them, at full price of $18, on the second or subsequent days. Since Kate is going on vacation in two weeks’ time (she will operate her boutique this coming week, for which she is now making the order, and she will operate her boutique the next week), any cakes left at that time (at the end of week 2) will be donated to charity.

Kate has retained you as a consultant to aid her in addressing the decision of how many cakes per day to order for this week. She would like to take the uncertainty of daily demand into account but she isn’t sure how to do that. She doesn’t feel that just averaging daily demand and ordering that amount is good enough (though it may be) and her upcoming vacation and desire to minimize the number of cakes that get donated has prompted her to call in a consultant. How many cakes per day should Kate order for this week?

Considerations

Remember that determining the best number to order this week should take into consideration what Kate is planning to do next week. Or vice versa.

1. How many cakes per day should Kate order for this week?
2. Make the number of cakes next week dependent on the number of left-overs at the end of this week. Does that change your estimate of how many should be ordered this week?
3. Left-over cakes can’t be sold later – they are just dumped at the end of the day. Does this change the number you want to order for this week?
4. Day-old cakes sell for $12 and two-day-old cakes are donated.

Answer rating: 100% (QA)

How many cakes per day should Kate order for this week ANS WER Kate should order 3 cakes per day for ... View the full answer