PLEASE USE EXCEL SOLVER $($SHOW FUNCTIONS$)$ A set of ten jobs must be scheduled at an integrated machining center that performs a number of metal$-$cutting operations on components for complex assemblies. These jobs and their processing and due times $($expressed in hours$)$ are shown in Table $2.$

As a result of the sequence chosen, each job will either be on time or else it will be late$/$tardy$.$ If it is late, the amount of time by which it misses its due date is called its tardiness.

a$.$ If the objective is to minimize the total tardiness in the schedule,

what is the minimum total tardiness and a sequence that achieves

it$?$

b$.$ If the objective is to minimize the number of tardy jobs in the schedule, what is the minimum number of tardy jobs and a sequence that achieves it$?$

c$.$ Add an ${11}^{th}$ job with a processing time of $25$ hours and a due time

of $35$ hours. Repeat part a$.$

d$.($This is a continuation of part c$.)$ Repeat part b$.$

e$.$ Comparing your answers for parts a and b to parts $c$ and $d,$ what is

the general effect on the solutions of adding that ${11}^{th}$ job? Do the

values of the objective functions get worse? Where does the ${11}^{th}$ job

get fit into the optimal sequences? Which objective function $($either

min total tardiness or min number of tardy jobs$)$ is better able to

handle this ${11}^{th}$ job being added?