Optimisation Problems

Optimization in design, economics and biological scenarios

QUESTION #1

The figure to the right illustrates a grass field. Answer the following:

Open Ended

What dimensions will maximise the area of the field?

QUESTION #2

^{The figure to the right shows a net enclosure for practising golf shots. The enclosure is open at one end, as shown. Answer the following:}

Open Ended

Find the dimensions that will minimise the amount of netting needed and give a volume of 432m^2.

(Netting is required only on the sides, the top, and the far end.)

QUESTION #3

A Heaven & Earth tin, illustrated to the right, must have a capacity of 1000 cm^3. Answer the following:

Open Ended

Determine the dimensions that require the minimum amount of production material. According to the marketing department, the smallest can that the market will accept has a diameter of 6 cm and a height of 4 cm. (Assume no waste material is left)

QUESTION #4

A glass box with a square base and no top must have a volume of

20 000 cm^3. Answer the following:

Open Ended

If the smallest dimension of the box is 10 cm, determine the dimensions of the box that will minimise the amount of glass required for this production.

QUESTION #5

^{Ocean Spray wants to produce a can that has the ability to hold 500 cm^3 of apple juice. Answer the following:}

Open Ended

The height of the can must be between 6 cm and 15 cm, inclusive. How should the can be constructed so that a minimum amount of material will be used in the construction?

(Assume that no waste is left.)