Henrique Correa\'s bakery prepares all its cakes between 4 A.M.and 6 A.M.so they

Question

Henrique Correa's bakery prepares all its cakes between 4 A.M.and 6 A.M.so they will be fresh when customers arrive. Day-old cakes are virtually always sold, but at a 50% discount off the regular $10 price. The cost of baking a cake is $7, and demand is estimated to be normally distributed, with a mean of 20 and a standard deviation of 8.

What is the optimal stocking level? The optimal stocking level for the bakery is ____ cakes (round your response to the nearest whole number).

MGMT 4353 POM FA17 mework | 24 of 25 (21 complete) Standard Normal Table table below shows the total area under the normal curve for a point that is Z standard deviations to the right of the 0.0 0.5000 0.5040 0.5080 0.51 0.1 0.5398 0.5438 0.5478 0.5617 0.5557 0.5596 0.5636 0.5675 05714 0.5754 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 10.6141 0.3 0.6179 0.6217 0.6255 0 6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517 0.4 0.6554 | 0.6501 | 0.6628 | 0.6664 06700 | 0.6736 | 0.6772 | 0.6808 | 0.6844 | 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 07157 0.71900.7224 0.7518 0.7549 0.7 0.7580 0.7612 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7996 0.8023 0.8051 0.8079 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 508 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 08708 0.8729 0.8749 0.8770 08790 0.8810 0.8830 12 0.8849 0.9015 | 1.3 0.9032 1090 9 10 9066 0.9082 0.9091 0.9115 | 09131 0.9147 09162 0.9177 09279 0.9292 0.9306 0.9319 1.0 0.8413 0.8438 0.8461 0.8485 0.8 0.8531 0.8554 0.8577 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 14 0.9192 09207 0.9222 0.9236 0.9251 0.9265 1.5 0.9332 0.9345 0.937 0.9370 09382 0.9394 0.9406 09418 09430 09441 1.6 0.9452 09463 0.947409485 0.9495 0.9505 09515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 09608 0.9616 0.9625 0.9633 0.9678 0.9686 0.96930.9 1.8 0.9641 0.9649 2.0- 0.9773 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0 1.9 0.9713 0.9719 0.9726 0.9732 09738 0.9744 0.9750 0.9756 0.9762 0.9767 Print Done

Explanation / Answer

This is a classic case of newsboy problem. If a news paper vendor keeps the excess stock he losses the money in form of cost of overstocking and if he keeps less stock, he losses money in form of oppurtunity cost

1. Cost of understocking (Cu) : 10 - 7 (Potential price - cost) = $3

2. Cost of overstocking (Co) : 7 - 5 (Cost - price) = $2

Balance would occur when expected benefit from selling extra cake will be less than the money it looses on understocking

P * Co < = 1-P *Cu

P <= Cu/ (Co+Cu)

P <= 3/5

P <= 0.6

On checking z table given in the problem, z score for 0.6 is ~ 0.254

Optimal Demand = Mean demand + z ( SD)

Demand = 20 + 0.254(8) = 22.03

Therefore, they should stock around 22 cakes

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