this is an optimization problem. please show all your work clearly.

Problem 3 Detroit Metro Airport needs to hire new employees. For the purposes of this problem, we will only consider a single day, as the real-world staffing problem is much more complex. DTW has identified the demand for workers D, for every hour from 4:00 am to 12:00 am (20 hours), defining each hour as a time period from period 1 (4:00 am - 5:00 am) to period 20 (11:00 pm - 12:00 am). The demand schedule is as follows: Di...,D5 = 5 De..... Dio = 20 D11,..., D15 = 25 D16,..., D20 = 15 Employees either work a full-time shift of 8 hours for $192 or a part-time shift of 4 hours for $84. Assume that workers can only start in 4-hour increments, at 4:00 am, 8:00 am, 12:00 pm, 4:00 pm, and 8:00 pm. A full-time worker can start a shift at 8:00 pm. Fractions of people cannot be hired. (a) Formulate a linear program in generic form to help DTW satisfy their demand for workers for the lowest cost possible. Make sure to define all variables and parameters clearly. (Hint: Use binary indicators to express whether demand can be covered by a given shift.) (b) Write the objective function in specific form. (c) Write the constraint(s) in specific form ONLY for the time period 2:00 pm - 3:00 pm Problem 3 Detroit Metro Airport needs to hire new employees. For the purposes of this problem, we will only consider a single day, as the real-world staffing problem is much more complex. DTW has identified the demand for workers D, for every hour from 4:00 am to 12:00 am (20 hours), defining each hour as a time period from period 1 (4:00 am - 5:00 am) to period 20 (11:00 pm - 12:00 am). The demand schedule is as follows: Di...,D5 = 5 De..... Dio = 20 D11,..., D15 = 25 D16,..., D20 = 15 Employees either work a full-time shift of 8 hours for $192 or a part-time shift of 4 hours for $84. Assume that workers can only start in 4-hour increments, at 4:00 am, 8:00 am, 12:00 pm, 4:00 pm, and 8:00 pm. A full-time worker can start a shift at 8:00 pm. Fractions of people cannot be hired. (a) Formulate a linear program in generic form to help DTW satisfy their demand for workers for the lowest cost possible. Make sure to define all variables and parameters clearly. (Hint: Use binary indicators to express whether demand can be covered by a given shift.) (b) Write the objective function in specific form. (c) Write the constraint(s) in specific form ONLY for the time period 2:00 pm - 3:00 pm