One of the many linear programming applications is in doing cost$-$to$-$benefit analysis. The

objective is to select a combination of benefits so as to minimize the cost $($premium$)$ while satisfying all

the benefits goals.

The decision variables here are the levels of four activities $($A$1,$ A$2,$ A$3$ and A$4).$ The linear

programming formulation looks like as below:

Minimize Total Cost $=2$A$1+$ A$2-$ A$3+3$A$4$

Subject to:

Benefit $1$: $3$A$1+2$A$2-2$A$3+5$A$480$

Benefit $2$: A$1-$ A$2+$A$410$

Benefit $3$: A$1+$ A$2-$ A$3+2$A$430$

A$1,$ A$2,$ A$3,$ A$4$ are algreater than or equal to $0.$

a$.$ Solve this problem using Solver, and save results and sensitivity analysis. Write down and interpret

the solution