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13 Nov 2019

14.

1. 8 ft

2. 5 ft.

3. none of the other answers

4. 6 ft

5. 7 ft.

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Elin Hessel
Elin HesselLv2
29 Jun 2019

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Related questions

DIRECTION:

Show all work – facts, primary and secondary equations, finding the derivatives, doing sign tests, and don’t forget to answer the questions asked!

1. A canvas wind shelter for the beach is to be constructed of 96 square feet of canvas that has been donated by a local company. The wind shelter is to have a back, two square sides and a top (see figure). What should be the dimensions of the shelter so that the space inside the shelter will be maximized?

2. A building supply store wants to build a rectangular outdoor storage facility on the rear wall of its building. An iron fence will enclose the facility on 3 sides and the wall of the building will be the fourth side. Find the dimensions of the storage facility with the largest area that can be built with 200 feet of fencing.

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

(a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes.



(b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.



(c) Write an expression for the volume V in terms of both x and y.

(d) Use the given information to write an equation that relates the variables x and y.

(e) Use part (d) to write the volume as a function of only x.

(f) Finish solving the problem by finding the largest volume that such a box can have.

Also:

A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence?

A box with a square base and open top must have a volume of 13,500 cm^3. Find the dimensions of the box that minimize the amount of material used.

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