optimization

A duck farmer wishs to build a rectangular enclosure of area 100m² . The famer must purchse wire netting for three of the sides, as the fourth side is an existing fence. Naturally, the farmer wishes to minimise the length (and therefore cost) of fencing required to complete the job.

If the sides adjacent to the existing fence have length x m, Write the equation for the length of wire netting to be purchased.

(in paper it will be L =, and we will use L for the following problems )

A duck farmer wishs to build a rectangular enclosure of area 100m² . The famer must purchse wire netting for three of the sides, as the fourth side is an existing fence. Naturally, the farmer wishes to minimise the length (and therefore cost) of fencing required to complete the job.

part b)

Find $$\frac{dL}{dx}$$

A duck farmer wishs to build a rectangular enclosure of area 100m² . The famer must purchse wire netting for three of the sides, as the fourth side is an existing fence. Naturally, the farmer wishes to minimise the length (and therefore cost) of fencing required to complete the job.

part c)

Find the minimum length of fencing needed to have an area of 100 m²

A 60 cm length of wire is bent into a rectangle with length x and width y.

We wish to maximum the area of rectangle created with this wire.

Write an equation to represent the Area of the rectangle in terms of x

A =

A 60 cm length of wire is bent into a rectangle with length x and width y.

We wish to maximum the area of rectangle created with this wire.

What is the maximum area this rectangle can be?

Sam has sheets of metal which are 36 cm by 36 cm square. He wants to cut out identical squares which are x cm by x cm from the corners of each sheet. He will ben the sheets along the dashed lines to form an open container.

Find the Volume equation of this container