1. Give the objective for this problem

2. Give the set of constraints that enforces the inventory balance requirements

3. Give the constraint(s) that require no more than 20,000 labor hours years 2 and 4 combined.

4. Give the constraint(s) that require year 2 to have the least labor hours among the four years.

5. Give the constraint(s) that required the storage level in year i to be lower than the storage level of its previous year for i = 2, 3, 4.

6. Give any other constraints necessary for a correct formulation of this problem.

The world is hit by a pandemic. Filead, a pharamceutical company has developed an effective drug and is planning its production of the drug over the upcoming years. The production facility can operate for four years, which we will denote years 1 through 4. The total available labor hours for the period of 4 years is 60,000 hours. The cost of producing drug in year i depends on the year earlier and later years are more cheaper than previous years. The production costs (per labor hour) and demands (in ml) are given as follows: Year Cost/hr Demand (in ml) 1 $ 610 60,000 2 $ 550 30,000 3 $ 400 10,000 4 $ 300 5,000 The demands must be met every year. Drug produced in year i can be used to meet demand in year i. Drug can also be produced in year i, stored, and used later. However, 15% of drugs put in storage is lost to wastage each year. So if 100 milliliters (ml) are stored in year i, only 85 ml are available in year i + 1. It costs $15/ml/year to store drug (paid on the ml of drugs put into storage). The storage capacity of the facility is 40,000 ml, i.e. there can't be more than 40,000 ml of drug stored at any given time. Drug production is 2 ml of drug per labor hour. There are additional constraints on production due to the availability of labor hours. These constraints are: No more than 20,000 labor hours can be used in years 2 and 4 combined. Storage level in year i must be lower than the storage level of its previous year for i = 2,...,4. Year 2 must have the least number of labor hours used in 4 years. It is feasible for year 2 to have the same number of labor hours as another year: it just cannot have more. The goal is to minimize the production and storage costs while satisfying all the constraints above. We will formulate this problem as a linear programming problem, using two sets of variables: Ii : labor hours used in year i, i = 1, ..., 4. Yi : ml of drugs put into storage in year i, i = 1,...,4. (please note units)