Array formula in B19:

=INDEX(Product, SMALL(IF(($C$11<=Price)*($C$12>=Price)*(OrderDate<=$C$16)*(OrderDate>=$C$15), ROW(Product)-MIN(ROW(Product))+1), ROW(1:1))) + CTRL + SHIFT + ENTER copied down as far as needed.

Named ranges

Price (B3:B6)
OrderDate (C3:C6)
Product (D3:D6)
What is named ranges?

Download excel file for this tutorial.

Lookup two index columns using min max value and a date range.xls
(Excel 97-2003 Workbook *.xls)

Functions in this article:

MATCH(lookup_value;lookup_array; [match_type]
Returns the relative position of an item in an array that matches a specified value

INDEX(array,row_num,[column_num])
Returns a value or reference of the cell at the intersection of a particular row and column, in a given range

MIN(number1,[number2])
Returns the smallest number in a set of values. Ignores logical values and text

SMALL(array,k) returns the k-th smallest row number in this data set.

ROW(reference) returns the rownumber of a reference

IF(logical_test;[value_if:true];[value_if_false])
Checks whether a condition is met, and returns one value if TRUE, and another value if FALSE

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