Your submission should consist of:

• A word-processed report of no more than 4 pages.

• Spreadsheet model clearly formatted and commented printable on one page.

All calculations and explanations must be clearly shown.

The work submitted must be your own work and any passages quoted. paraphrased or opinions relied upon must be properly attributed.

Situation

You are designing a simple vessel to store raw material for a production process. The vessel is cylindrical, with an open top and a conical bottom as shown in Fig. 1.

The required volume V of the container is 30 m³, to satisfy process feed requirements between raw material deliveries. The required diameter is 3 m to meet existing space requirements on the process.

Required

Find the optimum dimensions to minimise the cost of the vessel

State all assumptions that you make in formulating the problem. You may assume that the vessel cost is dependant only on the surface area of the tank.

Notes

V = Πr²(b/3 + h)

S = Πr(2h + √(b² + r²))