Gulliver produces explosives that are used in different mining companies. The fixed cost of is

R$100000$ and the variable cost is R$90$ per unit. The value of a is R$210$ and that of b is $0\mathrm{.}03.$

$($i$)$ calculate the optimal volume for this product and confirm that a profit occurs $($instead of a

loss$)$ at this demand. $(10)$

$($ii$)$ find the volumes at which breakeven occurs; that is$,$ what is the range of profitable demand?

Solve by hand.