Question 4 (19 points): Consider a multi-product production planning problem with setup cost where the following data/parameters are available: Parameters: 9tk : The fixed cost of producing any unit of product k in period t. Pik : Per unit purchase cost of product k in period i. hik : Per unit holding cost of product k in period i. TIK : Per unit shortage cost of product k for each period of shortage. TTK : Per unit lost sale cost for product k dkt : The demand of product k in period t. Shelf-life of product k Yk : The maximum number of shortage periods for product k (the number periods that the customer will wait to have her\his demand satisfied). Sets: T : The set of time periods in the planning horizon. K : The set of products Part a) Write a mathematical programming model to minimize the total cost of all products including purchase cost, holding cost, fixed cost, shortage cost, and lost sale cost. In your formulation, make sure that you consider the shelf-life of products and the maximum number of shortage periods. In your solution, you need to accurately define variables and new parameters/set (if required). (15 points) Part b) suppose that the volume of each product k is Sx (in cubic meters) and the total available space in the warehouse is F (in cubic meters). How would you modify the model to consider the limited space in the warehouse? (4 points) Question 4 (19 points): Consider a multi-product production planning problem with setup cost where the following data/parameters are available: Parameters: 9tk : The fixed cost of producing any unit of product k in period t. Pik : Per unit purchase cost of product k in period i. hik : Per unit holding cost of product k in period i. TIK : Per unit shortage cost of product k for each period of shortage. TTK : Per unit lost sale cost for product k dkt : The demand of product k in period t. Shelf-life of product k Yk : The maximum number of shortage periods for product k (the number periods that the customer will wait to have her\his demand satisfied). Sets: T : The set of time periods in the planning horizon. K : The set of products Part a) Write a mathematical programming model to minimize the total cost of all products including purchase cost, holding cost, fixed cost, shortage cost, and lost sale cost. In your formulation, make sure that you consider the shelf-life of products and the maximum number of shortage periods. In your solution, you need to accurately define variables and new parameters/set (if required). (15 points) Part b) suppose that the volume of each product k is Sx (in cubic meters) and the total available space in the warehouse is F (in cubic meters). How would you modify the model to consider the limited space in the warehouse? (4 points)