Consider the following linear program:

Variables:

Where, x$1$ is the number of units of Product $1$ produced.

Where, x$2$ is the number of units of Product $2$ produced.

Objective:

Minimize Cost

Constraints:

Constraint $1$: x$1+2$x$2<9$

Constraint $2$: $10$x$1+7\mathrm{.}5$x$2>50$

Constraint $3$: x$2>3$

Non$-$negativity: x$1,$ x$2>0$

The following Solver sensitivity analysis was generated:

a$)$ What is the optimal solution in number of units based on the sensitivity report above? $(1$ mark$)$

b$)$ Provide the formula of the objective function based on the table above and solve the objective function to determine the optimal value $(2$ points$)$

c$)$ Is it possible to determine the optimal value of the objective function if the coefficient of x$1$ changes from $8$ to $9$ and the coefficient of x$2$ changes from $10$ to $8?$ What is the effect on the optimal value as a result of these changes? $(2$ points$)$

d$)$ What will happen to the optimal value of the objective function if the objective function if Constraint #$3$ was increased from $3$ to $2?$ Interpret this change. $(2$ point$)$

e$)$ What will happen to the optimal value of the objective function if Constraint #$2$ was increased from $50$ to $55?$ Interpret this change. $(1$ point$)$