An interior beam with a rectangular cross section $450$ mm in height and $250$ mm in width is to be reinforced with $15$ M bars. The concrete has a compressive strength of $30$ MPa and the steel has a tensile strength of $400$ MPa. What are the maximum and minimum number of bars that could be used before risking brittle fracture? Assume one layer of reinforcement for this question. $($Hint: Find max and min area of reinforcement first.$)3.$ If $6$ bars and an aggregate size of $25$mm is used for question $2,$ will they need to be divided into two layers of reinforcing? $($show your work$)$ If so$,$ will two layers be enough? $($Hint: consider min cover and spacing.$)4.$ What is the maximum bending moment that can be carried by the beam from question $2$ with the reinforcement placement you determined in question $3?$