In a four$-$point flexural strength test, a $40-$inches long with a $2-$inches $($width$)$ by $5-$inches $($depth$)$ rectangle cross$-$section concrete beam is supported at the bottom by two supports that are $36$ inches apart $($span length$).$ Suppose the Modulus of Rupture of the concrete is $40{10}^6$ PSI.

a$.$ What is the maximum static load the beam can take when the load is applied, as shown below?

b$.$ What is the maximum static load the beam can hold if the beam is rotated $90$ degrees $($width changes to $5"$ and depth changes to $2")?$

c$.$ What is the maximum static load the beam can hold if the span length is changed to $32$ inches?