You own a coffee shop in a metro Toronto shopping mall. It is Friday evening and you are trying to decide how many dozen blueberry muffins to bake for the Saturday morning rush.
Based upon your experience with Saturdays, you think that the probability of being able to sell 5 dozen is 0.25, of being able to sell 10 dozen in 0.45, of being able to sell 15 dozen is 0.20 and of being able to sell 20 dozen is 0.10
A dozen muffins sells for $10.00 and has an incremental cost of $6.35. If you have leftover muffins, you will sell them to the local food bank for $2.00 per dozen.
1. Use your knowledge of decision analysis to model and solve this problem in order to recommend the number of dozen muffins that should be baked.
Please include the Payoff Table and all of the EMV calculations

Explanation:

What is given:

Demand  ProbCumulative Prob

5         0.250.25

10         0.450.70

15         0.200.90

20          0.101.00

Cost of underage or profit lost, Cu = Selling price - Cost per dozen = 10 - 6.35 = 3.65

Cost of overage or cost of a lost sale, Co = Cost per dozen - Salvage value = 6.35 - 2 = 4.35

The critical fractile CF = Cu / (Co + Cu) = 3.65 / (4.35 + 3.65) = 0.456

For the order quantity to become optimal it shoud be greater than or equal to the CF.

Let's see when this happens:

Demand (dozens)ProbCumulative Prob

5                         0.25  0.25 < 0.456

10                         0.45  0.70 > 0.456

15                         0.20  0.90

20                         0.10          1.00

This hapeens for 10 dozens of order size.

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