Problem $1(Cubic$ Cost Function$)$

A manufacturing company $is$ deciding $on$ the optimal level $of$ safety $S.In$ this

case, the cost increases $in$ a cubic manner, representing a steeper cost increase

$as$ safety levels rise. The profit function $is$:

$(S)=2200000-25(55000-200S)-500S^3$

Find the level $of$ safety $S$ that maximizes the company's profit.

Calculate the total cost when the optimal level $of$ safety $is$ chosen.

Calculate how much each worker will earn under the optimal safety level.

Calculate the total profit $at$ the optimal safety level.