10 points The administrator at the general hospital in Texas Presbyterian, Dallas (TPD) is ordering antidote...

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10 points The administrator at the general hospital in Texas Presbyterian, Dallas (TPD) is ordering antidote for copperhead bites for 2023. Based on prior experience, the admin has built the following probability table. The table below provides the likelihoods for the number of people who might be admitted for copperhead bites in TPD in 2023. Question 4: # of patients 10 11 12 13 14 15 16 Probability 0.10 0.20 0.22 0.20 0.15 0.1 0.03 TPD purchases these vials from the manufacturer Copperdote who charges $600/vial for any units ordered prior to January 2023. Because of biological reasons, unused vials of the antidote are thrown away in December 31st 2023. If the hospital has inventory of vials when a patient is admitted, the patient is administered the antidote from that inventory. In case, they do not have an antidote, they are required to purchase it from Copperdote on an emergency basis, and then administer the antidote. Any antidote purchased from Copperdote after the beginning of January 2023 costs $1600 per vial. Based on this information, answer the questions below 1. Suppose the current policy of TPD is to purchase 12 vials prior to January 2023. What is the expected cost associated with this policy? 2. What is the optimal number of vials that TPD should purchase prior to Jan 2023 that minimizes the overall expected cost for TPD? 3. What is the expected cost associated with this optimal policy? 10 points The administrator at the general hospital in Texas Presbyterian, Dallas (TPD) is ordering antidote for copperhead bites for 2023. Based on prior experience, the admin has built the following probability table. The table below provides the likelihoods for the number of people who might be admitted for copperhead bites in TPD in 2023. Question 4: # of patients 10 11 12 13 14 15 16 Probability 0.10 0.20 0.22 0.20 0.15 0.1 0.03 TPD purchases these vials from the manufacturer Copperdote who charges $600/vial for any units ordered prior to January 2023. Because of biological reasons, unused vials of the antidote are thrown away in December 31st 2023. If the hospital has inventory of vials when a patient is admitted, the patient is administered the antidote from that inventory. In case, they do not have an antidote, they are required to purchase it from Copperdote on an emergency basis, and then administer the antidote. Any antidote purchased from Copperdote after the beginning of January 2023 costs $1600 per vial. Based on this information, answer the questions below 1. Suppose the current policy of TPD is to purchase 12 vials prior to January 2023. What is the expected cost associated with this policy? 2. What is the optimal number of vials that TPD should purchase prior to Jan 2023 that minimizes the overall expected cost for TPD? 3. What is the expected cost associated with this optimal policy?