Final answer:
Cynthia Knot's oyster bar should use the newsvendor model to determine the optimal daily order quantity of oysters. This involves finding the critical ratio, looking up the corresponding z-score from the standard normal distribution, and calculating the order quantity by applying the z-score to the mean and standard deviation of the demand.
Step-by-step explanation:
The question asks how many pounds of oysters Cynthia Knot's oyster bar should order each day to maximize profits, factoring in that the demand for oysters follows a normal distribution with a mean of 100 pounds and a standard deviation of 14 pounds.
To determine the optimal order quantity, we need to calculate the newsvendor quantity, which balances the cost of overstocking (selling at a loss to her cousin) with the cost of understocking (lost sales of higher-priced oysters).
The newsvendor model requires the calculation of a critical ratio, which represents the probability of selling an item based on its cost and price. In this case, the profit of selling an oyster at the bar is $9 - $5 = $4 per pound, while the loss from having to sell unsold oysters to her cousin is $5 - $3 = $2 per pound.
The critical ratio is the profit divided by the total of profit and loss ($4/($4 + $2)) which is 0.6667, or 66.67%. We then use the inverse of the standard normal distribution to find the z-score that corresponds to this cumulative probability.
Once we find the z-score, we will calculate the order quantity by multiplying the z-score by the standard deviation and adding the result to the mean (100 pounds). This will give us the number of pounds Cynthia should order daily to maximize her profits while minimizing the risks associated with unsold inventory.