$(35$ points$)$ Construct a linear programming problem $($Problem title, problem idea, etc. This should be approximately two paragraphs.$)$ with ONLY your own student number as the parameters $($start from the last $2$ digits$-$use ONLY one or two digits' combinations$)$:

a$-$ Please formulate the model,

b$-$ Please solve this simplex method with Excel solver or Lingo software.

c$-$ Please show and explain the solution and sensitivity analysis results.

$*$This problem should be different from the midterm project.