Q$4.$ The Dreskin Development Company is building two apartment complexes. It must decide

how many units to construct in each complex subject to labor and material constraints. The

profit generated for each apartment in the first complex is estimated at $$900,$ and for each

apartment in the second complex, $$1,500.$ A partial initial simplex tableau for Dreskin is given

in the following table:

a$)$ Complete the initial tableau. $(5$ Points$)$

b$)$ Reconstruct the problem's original constraints $($excluding slack variables$)$ and write the

problem's original objective function. $(8$ Points$)$

c$)$ What is the basis for the initial solution? $(2$ Points$)$

d$)$ Which variable should enter the solution at the next iteration? Which variable will leave

the solution at the next iteration? $(4$ Points$)$

e$)$ How many units of the variable entering the solution next will be in the basis in the

second tableau? $(2$ Points$)$

f$)$ How much will profit increase in the next solution? $(4$ Points$)$