Zinc deficiency

A 56-year old woman presents to the clinic for loss of taste for the past 2 months. She states that she has been unable to taste or smell food so she has been eating much less than usual. She has also noticed that she has had hair thinning in the axillae and pubic area. Her past medical history is notable for alcoholic cirrhosis. Vitals are within normal limits. On physical exam, she has a sharply-demarcated red rash around the mouth and on the hands and buttocks. Which of the following nutrients is most likely deficient in this patient?