Consider the simply supported beam shown below.

The load carrying capacities of supports $1$ and $2$ are $12$ and $19$ kips, respectively $(1$

kip $=1000$ lbs$).$ The beam itself can withstand a bending moment of $65$ kip$-$feet, and

the maximum stress created by any loading is assumed to occur at one of the load

points $($a or b$).$

a$)$ Formulate a linear program that will determine the maximum possible load $($sum

of P$1$ and P$2)$ that this system can carry.

b$)$ Solve your model using Excel or LINDO.

c$)$ Assuming each kip of loading is worth $$1000,$ how much would you be willing to

spend to strengthen support $1?$