An architect is designing a cylindrical hotel that will have 150,000 square feet of floor space.

She wishes to make the hotel have as many 10-feet-high floors as possible, but the height of the building should not exceed 4 times its diameter or it might be unstable. (Fractional numbers of floors are acceptable in this rough analysis.)

(a) Formulate a mathematical programming model with 2 main constraints to choose an optimal design using decision variables x1! diameter of the hotel in feet and x2! number of floors.

(b) Enter and solve your model with the class optimization software.

(c) Using a 2-dimensional plot, solve your model graphically for an optimal design.

(d) On a separate 2-dimensional plot, show graphically that the problem becomes infeasible if the diameter is limited to 50 feet.