SOLUTION: I have to find the least expensive cost for a steel frame building which measures 600 cu. meters. The prices of horizontal beams are 20d and 30w, vertical beams are 50h. Thank yo

Question 164817: I have to find the least expensive cost for a steel frame building which measures 600 cu. meters. The prices of horizontal beams are 20d and 30w, vertical beams are 50h. Thank you.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The cost equation is

You also know that

You can replace one of the variables in the cost equation.

Then the cost equation becomes,

To minimize the cost function we have to find the partial derivative of C with respect to W and H and set those equal to zero.
1.
2.
The understanding is that and are partial derivatives.
From eq. 1,

3.
From eq. 2,

4.
From eq. 4,
4.

Substitute this expression in eq. 3 and solve for H,
3.

From eq. 4,

Finally,

The total cost would then be,

.... An interesting finding, minimizing cost means each portion makes up exactly 1/3 of the cost.

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