part 1)

A farmer is constructing a rectangular pen with two additional fences across it, separating it in three equal parts as shown below. Find the maximum area that can be enclosed in this way with 3200 m of fencing.

the maximum area is  m2?

 

part 2)

A fence must be built to enclose a rectangular area of 134640 m^2. Fencing costs $2.75 per meter for the two sides facing north and south, and $3.40 per meter for the other two sides. Find the size and cost of the least expensive fence.

The sides facing north and south should be  m long.

The other two sides should be  m long.

The fence will cost $

 

part 3)

Find the dimensions of the open-topped box with a square base that has volume 4 in^3 and requires the minimum amount of material to build.

(Hint: let x be the length of the base. Express the areas of the base and of four other sides in terms of x. Minimize the sum of these areas.)

The base of the box will have sides of length  in and the height of the box will be  in.

 

part 4)

An open box will be made by cutting a square from each corner of a 5 ft by 8 ft piece of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume?

(Hint: draw a diagram. )

 

part 5)

A closed box with a square box must be constructed so that its volume is 250 cm3cm3. The material for the top and the bottom of the box costs $8 per square cm. The material for the sides costs $4 per square cm.

a) Find the dimension of the box that will minimize the cost.

Answer: the base of the box will have sides of length  cm and the height of the box will be  cm.

b) Find the minimum total cost.

Answer: $