A skateboard manufacturer finds that the cost $C of making x skateboards per day can be modelled by the function C(x) = ax
2+bx+c

If 50 skateboards are made in a day, the cost of production is $1544.
The manufacturer noticed that making 12 skateboards in a day minimizes the cost of
production to $100.
a) Write C(x) in the vertex form. Hence, find the values of a, b and c.
b) What is the cost of production if no skateboards are made in a day?
c) What is the number of skateboards made in a day for a cost of production of $116?
d) What is the number of skateboards made in a day for a cost of production of at most $116?