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### 1 Answer

- 1 month ago
C = 15000 * sqrt(2^2 + x^2) + 5000 * (6 - x)

C = 5000 * (3 * sqrt(4 + x^2) + 6 - x)

We can minimize the cost, but that's calculus.

dC/dx = 5000 * (3 * (1/2) * 2x / sqrt(4 + x^2) + 0 - 1)

dC/dx = 0

0 = 5000 * (3x / sqrt(4 + x^2) - 1)

0 = 3x / sqrt(4 + x^2) - 1

1 = 3x / sqrt(4 + x^2)

sqrt(4 + x^2) = 3x

4 + x^2 = 9x^2

4 = 8x^2

1/2 = x^2

sqrt(2)/2 = x

C = 5000 * (3 * sqrt(4 + (1/2)) + 6 - sqrt(2)/2)

C = 5000 * (3 * sqrt(9/2) + 6 - sqrt(2)/2)

C = 5000 * (3 * 3 / sqrt(2) + 6 - 1/sqrt(2))

C = 5000 * (9/sqrt(2) - 1/sqrt(2) + 6)

C = 5000 * (8/sqrt(2) + 6)

C = 5000 * (4 * sqrt(2) + 6)

C = 5000 * 2 * (2 * sqrt(2) + 3)

C = 10000 * (2 * sqrt(2) + 3)

2 * sqrt(2) + 3 =>

2 * 1.414 + 3 =>

2.828 + 3 =>

5.828

10000 * 5.828 =>

58280

But none of that matters. You just need the formula for C, which is in line 2