A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 2400 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

x = 600 m

y = 1200 m

Amax = 720000  m²

Step-by-step explanation:

Let call x the smaller side of the rectangular plot and y the largest ( we assume we have one y side bounded by a river: Then

A(p)  Area of the plot x*y

A(p) = x*y

And perimeter of the plot ( to be fenced ) is:

P(p)  = 2*x + y = 2400     ⇒  y  = 2400 - 2*x

Area of rectangular plot as function of x:

A(x) = x * ( 2400 - 2x )

Taking derivatives on both sides of the equation

A´(x) = ( 2400 - 2x ) + (-2) *x    ⇒  A´(x) = ( 2400 - 2x ) - 2x

A´(x) = 0      ⇒   2400 - 4x = 0    ⇒  4x  = 2400  

x = 600 m

And y =  2400 - 2*x

y = 2400 - 1200

y = 1200 m

And the largest enclosed area is  Amax = 1200*600

Amax = 720000 m²

answer:

total cost for tiles and paints is $924.  

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

given: 1m squared floor tiles costs $3. so,

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

therefore, the combined total cost of tiles and paint is $924.