1. Heat oven to 375°F.
2. Beat butter and shortening in large bowl until blended. Add sugar, egg and vanilla; beat well. Stir together flour, baking powder, baking soda and salt; add to butter mixture, beating until well blended. Stir in pineapple, peanut butter chips and nuts, if desired. Drop by teaspoons onto ungreased cookie sheet. Lightly press cherry half in center of each cookie.
3. Bake 10 to 12 minutes or until lightly browned. Remove from cookie sheet to wire rack. Cool completely. Makes about 42 cookies.