Ackno Fenestrations manufacture garden conservatories to order. Their production costs per unit vary with the number of conservatories they produce per month according to the equation:
where y is the cost per conservatory in £, and x is the monthly output.
(a) Find the least cost level of output.
(b) Obtain the second derivative and use it to demonstrate that at the level of output you identify in (a) the cost per conservatory will be minimized.
(c) Work out the minimum cost per conservatory.