Thread: minimum cost

Greetings !

A closed rectangular box with a square box with a square base and with a capacity of 1.5 meter cubed is to be made The material for the top and bottom costs $3.00 per meter squared and for the sides is $4.00 per meter squared. Find the minimum cost.

I was able to get the 2 equations which are:

(x^2)(height) = 1.5
3x + 4h is a minimum

dx/dh = 3x + 6/x^2

then I equate this to zero

which gave me x = 4 and height = 0.09375

The cost of which is $12.375

But this is not a correct solution.

It is a multiple choice question, the selections are:

a. $36.68 b. $45.86 c. $28.68 d. $43.98

Any idea where I get wrong ?

Originally Posted by dugongster

Greetings !

A closed rectangular box with a square box with a square base and with a capacity of 1.5 meter cubed is to be made The material for the top and bottom costs $3.00 per meter squared and for the sides is $4.00 per meter squared. Find the minimum cost.

I was able to get the 2 equations which are:

(x^2)(height) = 1.5
3x + 4h is a minimum

This is wrong. The cost of the bottom is $3 per square meter, not per meter. The area of the bottom is $\displaystyle x^2$ square meters. The area of each side, and there are 4 sides, is xh square meters.

dx/dh = 3x + 6/x^2

then I equate this to zero

which gave me x = 4 and height = 0.09375

The cost of which is $12.375

But this is not a correct solution.

It is a multiple choice question, the selections are:

a. $36.68 b. $45.86 c. $28.68 d. $43.98

Any idea where I get wrong ?

I wonder why you thought "3x+ 4h" was the cost.

Aaah. Got 24/x + 6 x^2 is a minimum cost.

Differentiated it. Giving me x = cube root of 2, and h = cube root of 4

But still can't get a valid answer.