Determine the objective function for building a minimum-cost cylindrical tank of volume 160 ! and the height should be at least 2 longer than the radius, it should be noted that the cylindrical tank does not have a lid. If the circular ends cost $18 per " , the cylindrical wall costs $5 per " , and it is necessary to spray a protective material over the whole surface and inside of the tank at a cost of $30 per " . Moreover, due to safety restrictions, the total height of the tank must not exceed 10 m.

(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.