The Good Health Hospital has been able to secure two shipments of a vaccine against a novel variant of a certain infectious disease. Both shipments deliver the same vaccine. The first shipment is expected at the end of January and includes 500 doses. The second shipment is expected at the end of February and includes 900 doses. Your task is to determine the number of employees of each type vaccinated in January (shipment 1) and in February (shipment 2). The objective is to prioritize earlier vaccination of employees with higher exposure level to the disease. Note 1: You can assume that the allocation decision (who to vaccinate when) must be made on January 1 and the vaccine will be administered on the last day of the respective month. Each employee cannot receive more than one dose of the vaccine. Note 2: Even though it's tempting, your task in this problem is not to find the solution, but to formulate the model. Employee category (type) Type A: ICU staff Type B: General hospital staff Type C: Lab staff Number of employees 475 460 420 Exposure level 5 3 2 a) Formulate your model in words, indicating objective function, the decision variables, and constraints. (2 points) Please use linear optimization to answer questions b) d) below. b) Define the decision variables and formulate the objective function mathematically. (2 points) Provide a verbal justification for your choice of objective function coefficients. (1 point) c) Formulate your model constraints mathematically. (4 points) d) The GoodHealth Hospital has informed you that January vaccinations will be performed in batches of 20 employees. Only employees of the same category can be in a batch. Modify your model from a)-c) to account for this requirement. (2 points) e) Ignore part d). The lab director would like to add the following additional requirement: for each vaccine shipment, she wants the number of vaccinated General hospital staff to be at least double that of the ICU staff. Modify your model from a)-c) to account for this requirement. (2 points)