Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400 dozen roses. What is the number of states of nature for the payoff table?

Question

Quizplus · Accepted Answer

The number of states of nature is based on the possible outcomes. In this case, the possible outcomes are the demand for roses on Valentine's Day, which can be high or low. Therefore, there are two states of nature: high demand and low demand. 
To determine the best choice, we need to calculate the expected value of each decision based on the possible outcomes. The expected value is calculated as the sum of the products of the payoff for each outcome and the probability of that outcome. 
For each decision, the probabilities of high and low demand are uncertain, so we need to make assumptions or estimates. Let's assume there is a 50% chance of high demand and a 50% chance of low demand. 
For the decision to purchase 100 dozen roses: 
- If there is high demand, Blossom's Flowers can sell all 100 dozen roses for $20 a dozen, resulting in a payoff of $1,000. 
- If there is low demand, Blossom's Flowers can sell 100 dozen roses for $20 a dozen and 100 dozen roses for $5 a dozen, resulting in a payoff of $750. 
The expected value is: (0.5 x $1,000) + (0.5 x $750) = $875. 
We can calculate the expected value for the decisions to purchase 200 and 400 dozen roses in the same way:

- Purchase 200 dozen roses: expected value = (0.5 x $2,000) + (0.5 x $1,500) = $1,750. 
- Purchase 400 dozen roses: expected value = (0.5 x $4,000) + (0.5 x $3,000) = $3,500.

Based on these calculations, the best choice is to purchase 400 dozen roses, as it has the highest expected value.

Blossom's Flowers Purchases Roses for Sale for Valentine's Day