Figure 1: Table for Problem 1 BookWidth Height 1 10 1 2 22 3 20 T 4 5 6 7 15 7 Problem 2 (30 points). We need to build a bookcase composed of several shelfs, suitable to contain all the books as in the table of Figure 2; the books have different width and height. The width of the bookcase is fixed and equal to 40 (same units as the data in the table); the number of shelfs and their hight are instead variables of the problem, and need to be determined in order to fit all the books they will host: The higher each shelf is, the more expensive. Part I (20 points): Formulate a linear programming to minimize the overall cost of the bookcase so that it fits all the books in it. Part II (10 points): Solve the LP using Matlab (or any other solver at your choice). Provide i) the optimal solution; ii) the optimal objective value; and iii) the Matlab script used to solve the problem. 11 2 12 | 3 13 12 14 5 1 151 7 Figure 1: Table for Problem 1 BookWidth Height 1 10 1 2 22 3 20 T 4 5 6 7 15 7 Problem 2 (30 points). We need to build a bookcase composed of several shelfs, suitable to contain all the books as in the table of Figure 2; the books have different width and height. The width of the bookcase is fixed and equal to 40 (same units as the data in the table); the number of shelfs and their hight are instead variables of the problem, and need to be determined in order to fit all the books they will host: The higher each shelf is, the more expensive. Part I (20 points): Formulate a linear programming to minimize the overall cost of the bookcase so that it fits all the books in it. Part II (10 points): Solve the LP using Matlab (or any other solver at your choice). Provide i) the optimal solution; ii) the optimal objective value; and iii) the Matlab script used to solve the problem. 11 2 12 | 3 13 12 14 5 1 151 7