Your class diagram should look like this:
Class diagram consisting of 1) Preferred Customer, 2) Order, 3) CustomerShipment, 4) LineItem , 5) Shipment, 6) Product
Customers who place orders with us
Stepping through the solution from top to bottom, we start with customers who place orders with us.
The 0..* means that a customer may place zero or more orders and the multiplicity of 1 means that every order has to placed by one and only one customer.
An order is composed of one or more line items that refer to specific products. The line item would include things like the pricing and any applicable discount (1 multiplicity).
The line item identifies the specific product using the serial number (qualified association). A product might not ever be ordered, so the line item multiplicity is zero to one (0..1).
An order that is not filled completely will generate a backorder and associate that backorder with the order that it came from (reflexive association).
The order is shipped to the customer (customer shipment). When the order has not yet been shipped, the multiplicity is zero. When it takes a number of separate shipments to fill all of the order's items, original order plus backorders, the multiplicity is many (*).
Customer shipment is just one type of shipment (generalization). Another type is the incoming stock shipment referred to in the receiving process.
Products are stocked/stored in locations in our warehouse. Knowing a product, we can look up the location using a location ID (qualified association). Many products or no products may be in a given location (zero or more * multiplicity).
Finally, we can create new products using stock products, for example, a rack stereo system may consist of a receiver, CD player, speakers, etc. (aggregation).