Question

a regular storage container with an open top is to have a volume of 10 m^3 The length of the base is twice the width material for the base is $10 and the sides $6. find the cost of the materials for the cheapest such container

Answer 1

im completely lost plz help

Answer 2

No wonder, the problem is not clearly stated. For example, is the cost of the base material $10 per sq meter, or is it the total cost? Same goes for the sides, there are 4 sides with 2 of them twice the area of the other two. If it is as stated there is no calculations for the cost,the base $10 plus $6 for the sides, voila total cost $16.00 I don't think that is what they want, but still confusion exists.

Answer 3

This may be way out in left field. Let h = height, w=width, 2w=length.
Volume=(w)(2w)h=10 cubic meter or h= (10 cubic meter)/2w^2
Now the cost: base =2w^2=$10
sides (there are four)
2 are (wh) each
2 are (2wh) each
total sides 2wh+4wh=6$
cost: 2w^2+6wh=$16

now substitute (10 m^3)/(2w^2) for h in the cost equation

2w^2 (6w)(10)
----- + ------ =16
1 2w^2
Simplifying
2w^2 30
----- + --- =16
1 w

2w^3 +30=16w

2w^3-16w+30=0 dividing thru by 2
w^3-8w=15=0

differentiating
3w^2-8=0 solve and get w= approx 1.8
all other dimensions can now be solved by substitution.

I have some doubts about this due to the intermingling units (dollars and meters)