A TV manufacturer packs the finished TVs together according to their model types, and the dimension of the box for each model are as follows: Box Length 120 Dimension Width 100 Height 110 2 W|N 3 4 5 69 8 9 10 11 12 13 14 15 150 65 90 150 40 230 220 60 40 75 135 150 120 90 100 100 100 100 100 100 100 100 100 100 100 100 100 100 110 110 110 110 110 110 110 110 110 110 110 110 110 110 These boxes are going to be loaded into containers with dimensions 400 x 100 x 110 (Length X Width X Height). Since the products are fragile, rotating boxes is not allowed. Hence, you only need to consider the length dimension when loading. (a) (15 points) Develop a mathematical model to determine a loading plan such that the maximum unused (empty) space in a loaded/used container is minimized. Define your decision variables clearly. (b) (10 points) Solve the model (with a time limit of 60 seconds) you developed in part (a) using OpenSolver and report the best solution. Upload the excel file as well when uploading your solutions. (Hint: The best solution found within a time limit of 60 seconds has an objective function value of 55)