a$.$ Silppose the profit on Deluxe frames is increased from $$30$ to $$50.$

What is the optimal solution?

What is the value of the objective function when the unit profit is increased to $$50?$

b$.$ The unit profit on Professional frame were $$40$ instead of $$45,$ what is the optimal solutic the value of the objective function?

c$.$ What is the range of optimality of the profit from a Deluxe frame $($set$-$up and solve the inequalities for the slopes$).$

d: If the unit profit on Deluxe frames were $$20$ instead of $$30,$ would the optimal solution c use your answer for $(c)$