I need some help with this as soon as posible. I need to see the thought process

Question

I need some help with this as soon as posible. I need to see the thought process and tables of attempt to solve the problem. A detailed step by step explanation would be really appreciated.

Orders are delivered by trucks with capacity of 1200 units. One truck delivery costs $800 irrespective of the load. Alternatively, units can be shipped by courier at a cost of S2 each. A combination of the two types of delivery is also acceptable. Average inventory comes at a cost of S3 per average unit held in storage for the entire period. The fill rate is kept at 100%. Should the customer receive deliveries on Monday, or on Monday and Friday? Should the $3 increase or decrease for the two options to become indifferent? Why?

Explanation / Answer

The fill rate is the fraction of customer demand that is met through immediate stock availability, without backorders or lost sales. Here fill rate = 100% implies that all the orders need to be fulfilled.

When number of units = 800, the cost for both the channels (truck, courier) is the same. If number of units are less than 800, it is suggested to go with the courier option, i.e., deliver as and when the order arrives.

If the number of units to ship are > 800 then, collate all orders and ship them via truck (ship on Monday)

Since for the entire period the inventory cost remains same, it doesn't impact the way of delivery either through courier or truck.

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