Excel's Solver tool has been used to generate the sensitivity analysis report:

Variable Cells

Model

Final

Reduced

Objective

Allowable

Allowable

Variables

Name

Value

Cost

Coefficient

Increase

Decrease

X$1$

Deluxe

$15\mathrm{.}00$

$0\mathrm{.}00$

$10\mathrm{.}00$

$12\mathrm{.}50$

$2\mathrm{.}50$

X$2$

Professional

$17\mathrm{.}50$

$0\mathrm{.}00$

$15\mathrm{.}00$

$5\mathrm{.}00$

$8\mathrm{.}33$

Constraints

Final

Shadow

Constraint

Allowable

Allowable

Constraints

Name

Value

Price

R$.$H$.$ Side

Increase

Decrease

$1$

Aluminum

$100\mathrm{.}00$

$3\mathrm{.}13$

$100\mathrm{.}00$

$60\mathrm{.}00$

$46\mathrm{.}67$

$2$

Steel

$80\mathrm{.}00$

$1\mathrm{.}25$

$80\mathrm{.}00$

$70\mathrm{.}00$

$30\mathrm{.}00$

Based on the above solution, answer the following questions:

Determine the objective coefficient ranges.

Suppose the profit on deluxe frames is increased to $$20.$ Is the above solution still optimal? What is the value of the objective function when this unit profit is increased to $$20?$

If the unit profit on deluxe frames were $$6$ instead of $$10,$ would the optimal solution change?

Given that aluminum is a sunk cost, what is the maximum amount the company should pay for $50$ extra pounds of aluminum?