A small grocery store sells fresh produce, which it obtains from a local farmer. During the strawberry season, demand for fresh strawberries can be reasonably approximated using normal distribution with a mean of 40 quarts per day and a standard deviation of 6 quarts per day. Excess costs run 35 cents per quart. The grocery orders 49 quarts per day.

a)What is the implied cost of shortage per quart?
b)Why might this be reasonable figure?

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Given daily demand d=40 quarts per day

std dev =6 quarts
Ce= 35 cents
Service level =Cs/(Cs+Ce)
Optimal orders = mean demand + z * std dev
49 = 40 + z*6
=> z=0.6666
from standard normal diistribution table service level will be 0.748
=> Cs=104 cents.

a) To find the implied cost of shortage per quart, we need to calculate the probability of running out of strawberries and the corresponding cost.

Step 1: Calculate the z-score:
We know that the mean daily demand for strawberries is 40 quarts per day, and the standard deviation is 6 quarts per day. The grocery store orders 49 quarts per day.

To calculate the z-score, we use the formula:
z = (x - μ) / σ
where x is the desired value, μ is the mean, and σ is the standard deviation.

In this case, let's calculate the z-score when x = 49:
z = (49 - 40) / 6
z = 9 / 6
z = 1.5

Step 2: Find the probability of running out:
Using the z-score, we can determine the probability of running out of strawberries. We canlook up this value in a standard normal distribution table or use software such as Excel.

Using the z-score of 1.5, the probability of running out is approximately 0.9332.

Step 3: Calculate the cost of shortage per quart:
The cost of shortage per quart is the excess cost per quart multiplied by the probability of running out.

The excess cost per quart is 35 cents per quart.

Cost of shortage per quart = Excess cost per quart * Probability of running out
Cost of shortage per quart = 0.35 * 0.9332
Cost of shortage per quart ≈ 0.3266 cents per quart

Therefore, the implied cost of shortage per quart is approximately 0.3266 cents per quart.

b) This reasonable figure can reflect the cost of not meeting the demand for strawberries. Since the store sells fresh produce, customers may be disappointed if the strawberries run out, leading to potential loss of sales and customers. In the case of shortage, the store may also have to spend effort in managing customer complaints or finding alternative solutions. Hence, the cost of shortage per quart helps identify and quantify the potential impact of not meeting the demand accurately, providing useful information for decision-making and planning to meet customer expectations.

a) The implied cost of shortage per quart can be calculated by determining the probability of running out of strawberries and multiplying it by the excess costs per quart. To calculate the probability of running out, we need to find the z-score representing the difference between the demand and the ordered quantity, and then use a standard normal distribution table to find the corresponding probability.

First, let's calculate the z-score:
z = (49 - 40) / 6
z = 1.5

Next, we look up the probability associated with the z-score of 1.5 in a standard normal distribution table. The table tells us that the probability is approximately 0.9332.

Since this is the probability of not running out of strawberries, the probability of running out is 1 - 0.9332 = 0.0668.

Finally, we multiply the probability of running out by the excess costs per quart:
Cost of shortage per quart = 0.0668 x $0.35 = $0.0234

Therefore, the implied cost of shortage per quart is approximately $0.0234.

b) This can be considered a reasonable figure because it takes into account the potential loss in sales from not having enough strawberries to meet the demand. The grocery store incurs a cost for each quart that is not available for purchase, which represents a missed opportunity to generate revenue. By calculating the cost of shortage per quart, the store can analyze the financial impact of not meeting the demand and make more informed decisions regarding inventory management and ordering quantity.