You are a statistician working at a small, but premium gourmet bakery. Your bakery can produce up to 4 elaborate custom wedding cakes per week (constrained by design time, bake time, and craft time). If weekly demand is greater than the four cakes you can make, you lose sales as the customers will order from the inferior-but-faster Amazon Baking Company instead (so, there are weeks that the demand for your cakes is not met). Each wedding cake costs 300 dollars (labor + materials) to produce, but sells for $1000. You estimate that the probability distribution of weekly demand for custom wedding cakes is as follows: Demand 0 1 2 3 4 5 6 7 Probability 0.05 0.05 0.10 0.20 0.40 0.10 0.05 0.05 What is the expected profit each week from wedding cake sales? (Hint: Remember, some sales will go elsewhere if you are at maximum crafting capacity.)
You are a statistician working at a small, but premium gourmet bakery. Your bakery can produce up to 4 elaborate custom wedding cakes per week (constrained by design time, bake time, and craft time). If weekly demand is greater than the four cakes you can make, you lose sales as the customers will order from the inferior-but-faster Amazon Baking Company instead (so, there are weeks that the demand for your cakes is not met). Each wedding cake costs 300 dollars (labor + materials) to produce, but sells for $1000.
You estimate that the probability distribution of weekly demand for custom wedding cakes is as follows:
| Demand | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Probability | 0.05 | 0.05 | 0.10 | 0.20 | 0.40 | 0.10 | 0.05 | 0.05 |
What is the expected profit each week from wedding cake sales? (Hint: Remember, some sales will go elsewhere if you are at maximum crafting capacity.)
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