Optimization Problems (So confusing) Please me on this once. Thanks in a million

1. Nov 8, 2004

eagle_johny

Optimization Problems (So confusing) Please me on this once. Thanks in a million !!!!

The Dome Tent
1 .Imagine making a tent in the shape of a spherical cap (a sphere with lower portion sliced away by a plane). Assume we want the volume to be 2.2 m^3, to sleep two or three people.
a. make a sketch of this tent, identifying all appropriate variables
The floor of the tent is cheaper material than the rest: assume that the material making up the dome of the tent is 1.4 times as expensive per square meter than the material touching the ground
b. determine and graph a function, which gives that cost of the tent material as a function of an appropriate variable
c. what should the dimensions of the tent be so that the cost of the material is a minimum?
d. what is the total area of the material used for this minimum cost tent?
e. now consider a dome tent in which the floor is more expensive than the rest of the tent material” assume that the material touching the floor is 1.4 times as expensive per square meter than the material making up the dome of the tent. Carry out steps a) b) and c) above for this tent
f. how practical would each of these two tents be?

The pup tent
Now consider making a tent in the shape of a right prism whose cross section is an equilateral triangle (the door is on one on of the triangular ends). Assume once again that the volume is 2.2 m^3, to sleep two or three people. Please answer questions a) through f) above this tent design (for this tent the phrase “material making up the ends and top” should be substituted for the phrase “the material making up the dome”

Thank you thank you thank you

2. Nov 8, 2004

Justin Lazear

The radius of the sphere and the distance into the sphere are the variables, although one will actually depend on the other in order to maintain a constant volume.

Can you find an expression that gives you surface area in terms of radius and the distance the plane cuts away?

--J

3. Nov 8, 2004

eagle_johny

no. I'm stuck with these two problems. :(