Question 1: The local bookstore must determine how many of each of the four new books on photonics it must order to satisfy the new interest generated in the discipline. Book 1 costs $50, will provide a profit of $10, and requires 3 inches of shelf space. Book 2 costs $70, will provide a profit of $12, and requires 8 inches of shelf space. Book 3 costs $80, will provide a profit of $8, and requires 2 inch of shelf space. Book 4 costs $65, will provide a profit of $15, and requires 2 inches of shelf space. Find the number of each type that must be ordered to maximize profit. Total shelf space is 620 inches. Total amount available for ordering is $9500. It has been decided to order at least 20 Book 3. (1) Establish the model of the optimisation problem. State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent. (2) Suppose the number of Book 3 is half the number of Book 1, and the number of Book 4 is fixed as 13, establish the model of the new optimisation problem., (3) For the model established in step (2), obtain the graphical solution using MATLAB. (4) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again. Question 2: Determine the objective function for building a minimum-cost cylindrical tank of volume 60m? and the height should be at least 2m longer than the radius, it should be noted that the cylindrical tank does not have a lid. If the circular ends cost $12 per m? , the cylindrical wall costs $5 per m? . the reinforcement cost for the base is $20 per m?2, and it costs $30 per m? for the protecting material over the whole surface (double sides). Additionally, the base requires an extra 10% of its total cost for transportation and installation fees. (1) Establish the mathematical model of the optimisation problem. State clearly in words what the decision variables are, what the objective function and the equation/inequality constraints represent. (2) Draw the graphs and find the optimal solution (graphical solution). (3) Change one of the parameters to cause the optimal solution (optimal design variables) changes and solve the problem again. (4) If this tank needs a lid, rebuild the mathematical model and solve the problem again. For questiont: o For sub-question (1), write the model of the optimisation problem (0.5 marks), describe the decision variables, objective function, and equality/inequality constraints (1 mark) 0 Solve sub-question (2) (0.5 marks) o For sub-question (3), find the optimal solution by the code of MATLAB and give an image of the graphical solution (2 marks) For sub-question (4), find the optimal solution and write the values of the design variables, objective function, and equality/inequality constraints (0.5 marks). Given the corresponding code and the image of the graphical solution (0.5 marks) For question 2: o For sub-question (1), write the model of the optimisation problem (0.5 marks), describe the decision variables, objective function, and equality/inequality constraints (1 mark) 0 Solve sub-question (2), find the optimal solution by the code of MATLAB and give an image of the graphical solution (1.5 marks) o For sub-question (3), find the optimal solution and write the values of the design variables, objective function, and equality/inequality constraints (0.5 marks). Given the corresponding code and the image of the graphical solution (0.5 marks) o If this tank needs a lid, rebuild the mathematical model (0.5 marks) and solve the problem again (0.5 marks). Include the code with proper comments in line to explain each code line that you have written to solve each question and attach it with the report