Consider the following optimal simplex tableau of a maximization problem of total profit $($$$)$ with $<=$ constraints

and main decision variables $!,".$

Basic Z $!"$# $$$ $\%$ Right Side

Z $1007\backslash$alpha $0$

$!01050-218$

$$$ $0\backslash$beta $01/21411$

$"0060024$

Part a$)$ List the optimal solution for decision variables. Identify special cases if any.

Part b$)$ Find the values for $\backslash$alpha $,\backslash$beta $,$ and $.$

Part c$)$ Find shadow prices and explain their meaning and application.

Part d$)$ If you could buy two additional units of the first resource for total cost of $$3,$ would you do this? Why?

Part e$)$ Given the table above, which one of the followings can be a possible dual for this problem?

$1.$ Minimization problem with $2$ variables and $3$ constraints

$2.$ Maximization problem with $2$ variables and $3$ constraints

$3.$ Minimization problem with $3$ variables and $2$ constraints

$4.$ Maximization problem with $3$ variables and $2$ constraints