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A handwritten solution showing $($a$)$ the free body diagram of the beam; $($b$)$ the equilibrium equations that you used to calculate the reactions at the supports; $($c$)$ internal loading diagram for three sections of the beam; and $($d$)$ equations for the shear force and bending moment as a function of x$.$ To check your solution use that when a $=$ L$/3=7$ ft$,$ the maximum magnitude of the bending moment is $9\mathrm{.}80$ kip$-$ft$.$

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Create a MATLAB program or Excel sheet to calculate the maximum bending moment as function of x for $0$a$7$ ft$.$ Feel free to include any additional values in the program or Excel sheet$$ if you need them for your calculations.$$ Verify that your computer based solution has the correct values for a $=7$ ft$.$ Use your data to identify the maximum magnitude of the bending moment for different values of a$.$ Identify the value of a that produces the lowest maximum magnitude of the bending moment and the corresponding value for the maximum magnitude of the bending moment Create a graph in either Excel or MATLAB of the the maximum magnitude of the bending moment as a function of x for $0$a$7$