Solve this problem using by hand using the simplex algorithm using matrix form. Starting

with your optimal solution to this problem, do the work by hand to answer each of the

following questions:

$($a$)$ You are practicing for a baking competition, and your boss has said that they are willing

to modify the baking schedule so that you can get some extra practice. You need to

bake at least one of each type of cake. Show that these additional restrictions make

the current solution infeasible, then use the dual simplex to find the new feasible and

optimal solution.