The optimization process and recommendations:

1. Avoid Subqueries (query line: 22): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

CREATE INDEX chargeitems_idx_workitem_id ON dbo.ChargeItems (WorkItem_Id);
CREATE INDEX workitems_idx_dmc ON WorkItems (DMC);

The optimized query:

SELECT
        [Limit1].[Id] AS [Id],
        [Limit1].[DMC] AS [DMC],
        [Limit1].[FirstSeen] AS [FirstSeen],
        [Limit1].[DrawingNo] AS [DrawingNo],
        [Limit1].[MachineId] AS [MachineId],
        [Limit1].[WorkItemState_Id] AS [WorkItemState_Id],
        [Limit1].[ItemType_Id] AS [ItemType_Id],
        [Limit1].[Repaired] AS [Repaired],
        [Limit1].[MachineCycle] AS [MachineCycle],
        [Limit1].[FirstSeenCheck] AS [FirstSeenCheck],
        [Limit1].[LastSeen] AS [LastSeen],
        [Limit1].[Archive] AS [Archive],
        [Limit1].[CastingDateString] AS [CastingDateString],
        [Limit1].[Deleted] AS [Deleted],
        [Limit1].[DMC2] AS [DMC2],
        [Limit1].[Id1] AS [Id1],
        [Limit1].[WorkPlace_Id] AS [WorkPlace_Id],
        [Limit1].[CastingFormIdent_Id] AS [CastingFormIdent_Id],
        [Limit1].[FormIdentItemType_Id] AS [FormIdentItemType_Id] 
    FROM
        (SELECT
            TOP (1) [Extent1].[Id] AS [Id],
            [Extent1].[DMC] AS [DMC],
            [Extent1].[FirstSeen] AS [FirstSeen],
            [Extent1].[DrawingNo] AS [DrawingNo],
            [Extent1].[MachineId] AS [MachineId],
            [Extent1].[WorkItemState_Id] AS [WorkItemState_Id],
            [Extent1].[ItemType_Id] AS [ItemType_Id],
            [Extent1].[Repaired] AS [Repaired],
            [Extent1].[MachineCycle] AS [MachineCycle],
            [Extent1].[FirstSeenCheck] AS [FirstSeenCheck],
            [Extent1].[LastSeen] AS [LastSeen],
            [Extent1].[Archive] AS [Archive],
            [Extent1].[CastingDateString] AS [CastingDateString],
            [Extent1].[Deleted] AS [Deleted],
            [Extent1].[DMC2] AS [DMC2],
            [Extent1].[WorkPlace_Id] AS [WorkPlace_Id],
            [Extent1].[CastingFormIdent_Id] AS [CastingFormIdent_Id],
            [Extent1].[FormIdentItemType_Id] AS [FormIdentItemType_Id],
            [Extent2].[Id] AS [Id1] 
        FROM
            WorkItems AS [Extent1] 
        LEFT OUTER JOIN
            [dbo].[ChargeItems] AS [Extent2] 
                ON [Extent1].[Id] = [Extent2].[WorkItem_Id] 
        WHERE
            (
                [Extent1].[DMC] = ''
            ) 
            OR (
                (
                    [Extent1].[DMC] IS NULL
                )
            )) AS [Limit1]