Question $112\mathrm{.}5$ pts

An auto part manufacturer is now paying much more attention to the transit time between one processing stage and the next. There are four machines that perform a certain processing phase, and three machines that perform the next phase. All units of a large class of cars go through these two phases.

The table below displays the transit time, in minutes, from each machine of the first phase $($P$1)$ to each machine of the second $($P$2).$ Mach $3$ is not really $95$ minutes away from machine B$,$ but the company has prohibited that combination because of quality problems associated with that specific pairing $($so the $95$ is entered into the problem$).$ Supply and demand quantities are in cars processed per week. Develop a transit time minimizing solution for this firm.

P$2,$ Mach AMach BMach CSUPPLYP$1,$ Mach $19\mathrm{.}534700$Mach $247\mathrm{.}55\mathrm{.}5600$Mach $33\mathrm{.}59551000$Mach $476\mathrm{.}53700$DEMAND$12501475900$

a$.$ What is the least transit time of this solution? $[$ Select $]["10,980","10,925","11,485","11,325","11,200"]$

b$.$ Which machine in Phase $2$ did not meet its required demand? $[$ Select $]["$Machine B$",$ "Both Machine C and A$",$ "All demands are met", "Machine C$",$ "Machine A$"]$

c$.$ Which machine in Phase $1$ has some capacity unused? $[$ Select $]["$Machine $1",$ "Machine $3",$ "Machine $2",$ "None has any supply remaining", "Machine $4"]$

d$.$ Was the prohibition on the Mach $3-$ Mach B combination honored? $[$ Select $]["$Yes$",$ "cannot determine based on the information given", $"$No$"]$

e$.$ What if you now required $75$ units to be shipped from Mach $4$ to Mach A$.$ What is the optimal solution? $[$ Select $]["$$$9,893\mathrm{.}00",$ "same as the original solution", $"$$$11,337\mathrm{.}50","$$$12,500\mathrm{.}67","$$$10,950\mathrm{.}75"]$