Identify the appropriate inventory model to obtain the optimal lot size for the given problem description: Rick Jones is chairman of this year’s Walk for Diabetes event. Each year, the organizers of the event typically have commemorative T-shirts available for purchase by the entrants in the walk. Rick needs to order the shirts well in advance of the actual event. Based on past walks, the organizers have determined that the demand for Tshirts is normally distributed with a mean of 100 and a standard deviation of 10. Rick plans to sell the T-shirts for $20 each. He pays his supplier $8 for each shirt and can sell any unsold shirts for rags at $2 each. Determine how many T-shirts Rick should order to maximize his expected profits

In this question, the T-shirts rick should order to maximize his expected profits is 104 in quantity. The appropriate inventory model would be single period.

What do you mean by the inventory model?

Inventory models deal with the quantity of the order as well as the moment at which it should be placed. The issue at hand is how to make these choices as economically as possible while accounting for the price of acquiring the items, the price of keeping a unit on hand, and the price of shortages.

The accuracy that inventory management models provide is important. You may learn which products are selling and which are not, which ones you must have on hand, and the precise quantity needed.

Here,

Cu = 20 - 8 = 12,

Co = 8 - 2 = 6

Critical ratio = Cu/ (Cu + Co) = 12/ (12 + 6) = 0.6667

Z value corresponding to 0.667 = 0.4307

Order quantity = 100 + 10 × 0.4307 = 104

Therefore, in this question, the T-shirts rick should order to maximize his expected profits is 104 in quantity. The appropriate inventory model would be single period.

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