Question

The total cost of producing a type of boat is given by C(x)=13000−10x+0.01x2, where x is the number of boats produced. How many boats should be produced to incur minimum cost?

Answer 1

500

Explanation:

The total cost of producing a type of boat is given by C(x) = 13000 - 10x + 0.01x²........ (1), where, x is the number of boats produced.

Now for cost to be minimum
`(dC)/(dx) =0`

So, differentiating equation (1), we get - 10 + 0.02x = 0

⇒ x =
`(10)/(0.02) =500`

Therefore, 500 total boats should be produced to incur minimum cost. (Answer)