nsitivity Analysis Questions: Price change

a$)$ Suppose 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?$

Assume the profit from Professional frame remains at $$45($i$.$e$.$ no change to profit per unit$).$

b$)$ If the unit profit on Professional frame were $$40$ instead of $$45,$ what is the

optimal solution and what is the value of the objective function?

Assume the profit from Deluxe frame remains at $$30($i$.$e$.$ no change to profit per unit$).$

c$)$ What is the range of optimality of the profit from a Deluxe frame. That is$,$

assume that c be the profit per unit of a Deluxe frame. Currently, c $=30.$

Assume that the profit from one unit of the professional frame is fixed at its

current value of $$45.$ Determine the lower and upper limits for c so that the

current optimal solution remains optimal.

d$)$ If the unit profit on Deluxe frames were $$20$ instead of $$30,$ would the

optimal solution change?

Assume the profit from Professional frame remains at $$45($i$.$e$.$ no change to profit per unit$).$