Question 2:

Determine the objective function for building a minimum-cost cylindrical tank of volume

160m³ 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 $18 per m², the cylindrical wall

costs $5 per m², and it is necessary to spray a protective material over the whole surface and

inside of the tank at a cost of $30 per m². 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.