$7-10$ A linear program has the objective of maximizing

profit

$=$

$12$

$$

$+$

$8$

$$

$.$

The maximum profit is $$8,000.$ Using a computer, we find the upper bound for profit on X is $20$ and the lower bound is $9.$ Discuss the changes to the optimal solution $($the values of the variables and the profit$)$ that would occur if the profit on X were increased to $$15.$ How would the optimal solution change if the profit on X were increased to $$25?$