Suppose a supply chain that consists of a supplier and a retailer. The supplier produces a product at the cost of $5 per

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Suppose a supply chain that consists of a supplier and a
retailer. The supplier produces a product at the cost of $5 per
unit. which is sold to the retailer at $10. The retailer, in turn,
sells the product to final customers at $12. The demand for the
product is normally distributed with mean 400 and standard
deviation 100. Any leftover items at the retailer will be returned
back to the supplier who in turn salvage them at $3 per item
The two firms agree to establish vendor-managed inventory. That
is, instead of the retailer placing an order. the supplier
determines the number of products to be produced （and stocked) in
the retailer's warehouse. The retailer no longer makes inventory
decisions. Assume that the supplier tries to maximize its own
profit. How many products would the supplier produce and stock at
the retaller? Choose the nearest number.
*Newsvendor problem question
A. 491
B. 400
C. 432
D. 470
E. 457