Question

Demand of a product is normal with mean 4000 and standard deviation of 150. the manufacturer decides to use postponed product differentiation. Therefore, she produces unfinished items with the cost of $5, and finishes the product after getting the order from the customers with the cost of $3. The manufacturer can sell the finished product at $10. However, unused base products at the end of the season can be soid at $2 only. For any product she feels she has iost money because of the capital tied up in the inventory for the whole season. She estimates a loss of $0.20 for every dollar tied up in a product that must be sold off at the end of the season. How many base products should she produce at the beginning of the season?

A. 1000
B. 2000
C. 3000
D. 4000

Answer 1

To find the optimal number of base products to produce, the manufacturer should analyze expected profits at different inventory levels and choose the one that maximizes expected profit. This involves considering production costs, costs of capital tied up in inventory, and the end-of-season sell-off value. The use of the news-vendor model and demand distribution data is critical in this process.

Step-by-step explanation:

Calculating Optimal Inventory Level

To determine how many base products the manufacturer should produce at the beginning of the season, it is necessary to perform an analysis of the expected profit for each level of inventory, given the costs and revenues associated with production, finishing, selling, and potential end-of-season offloading.

The product has a known demand distribution with a mean (μ) of 4000 and a standard deviation (σ) of 150. The fixed cost for producing an unfinished base product is $5, with an additional $3 for finishing the product upon receiving an order. The finished product sells for $10, while the excess inventory can be sold for $2 at the end of the season, with an additional cost of $0.20 for every dollar tied up in inventory.

To maximize profit, the manufacturer must balance the risk of producing too many items (leading to excess inventory) against producing too few (leading to lost sales). The correct balance should equate to the point where the marginal cost of producing an additional unit equals the marginal revenue from selling that unit. This calculation is complex and generally requires understanding of concepts like news-vendor model, which uses the demand distribution to find the optimal order quantity that maximizes expected profit, or minimizes the expected cost.

In this scenario, to find the optimal inventory level one would typically calculate expected profits (or costs) at various production levels, considering the costs of production, the costs of capital tied up in inventory, and the sell-off value for excess items. The level that results in the maximum expected profit would be the optimal quantity to produce. The problem provides four choices, but without further information, we cannot determine the exact number of items to produce from these options.