Optimisation

[gabiorrico]

Imagine making a tent in the shape of a right prism whose cross section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.2 m³, to sleep 2 or 3 people. Draw a picture identifying all appropriate variables. The floor of the tent is cheaper material than the rest: assume that the material making up the top and the ends of the tent is 1.4 times as expensive per square metre than the material touching the ground.

a. What should the dimensions of the tent be so that the cost of the material used is a minimum?

b. What is the total area of material used?


Now change the problem so that the floor of the tent is more expensive material than the rest: assume that the material touching the ground is 1.4 times as expensive per square metre than the material making up the ends and the top of the tent.

c. What should the dimensions of the tent be so that the cost of the material used is a minimum?

d. What is the total area of the material used?

 

[tkhunny]

That's an excellent problem. You should get started.

Looking at the base, we have a Rectangle. Length = L, Width = W, Area = L*W
Looking at the end, we have an Equilateral Triangle. Side = W, since we already defined this for the floor. You tell me the height and the surface area.
As it turns out, the two sides are exactly the same size as the floor.

Okay, now what?