Question

Cynthia Knott's oyster bar buys fresh Louisiana oysters for $5 per pound and sells them for $9 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $2 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 100 pounds and a standard deviation of 15 pounds. How many pounds should she order each day?

Answer 1

Answer:

103

Explanation:

Please see attachment .

Answer 2

The number of pounds to be ordered each day is 103 pounds. This is calculated using the news vendor model.

What is the news vendor model?

The news vendor model is used to determine the optimum inventory level in case of uncertainties. The level of inventory is calculated using z score of the probability. The probability under this model can be calculated as:

$\rm P = \dfrac{Co}{Cu+Co}$

Where Co is the cost of actual Utilization, and Cu is the cost of under Utilization.

$\rm Co = Selling\:price - Cost\\\\\rm Cu = Cost - Receipt\:from\:sale\:of \:unsold\:stock$

The quantity can be calculated as:

$\rm Quantity = Mean + (Standard \:deviation \times z\: score\: of \:probability)$

The z score of probability can be calculated from the table.

Given:

Mean is 100

Standard deviation is 15

Cost is $5

Selling price is $9

Selling price of unsold stock is $2

Therefore Co and Cu will be:

$\rm Co = Selling\:price - Cost\\\\Co = \ 9 - \ 5\\\\Co= \ 4$

And,

$\rm Cu = Cost - Receipt\:from\:sale\:of \:unsold\:stock\\\\ Cu = \ 5 - \ 2\\\\ Cu = \ 3$

The probability will be:

$\rm P = \dfrac{Co}{Cu+Co}\\\\\rm P =\rm \dfrac{\rm Co}{\rm Cu+Co}\\\\\rm P = 0.5914$

The z score of this probability is 0.18

Therefore the quantity will be:

$\rm Quantity = Mean + (Standard \:deviation \times z\: score\: of \:probability)\\\\\rm Quantity = 100+ (15\times 0.18)\\\\\rm Quantity = 100+ 2.7\\\\\rm Quantity = 102.7 \\\\\rm Quantity = 103\:pound$

Learn more about news vendor model here:

https://brainly.com/question/3964633