$(25$ pts$.)$ Consider the values shown in the $8-$month table below. Assume: $I_0=300$

$D_t,I_0,$ Q in units; $c_t$ in $\frac{\text{\$}}{?}$ unit $($to purchase or produce$)$; $A_t$ in $\frac{\text{\$}}{?}$ order; $h_t$ in $\frac{\text{\$}}{?}$ unit$/$month

a$.$ Find the $8-$month production schedule and resulting cost based on the Lot$-$for$-$Lot rule.

b$.$ Find the $8-$month production schedule and resulting cost by the Fixed Order Quantity rule $(Q=1,500).$

c$.$ Explain briefly if and under what conditions a Just in Time $($JIT$)$ policy might make sense in this

production company.

d$.$ Suppose the total demand for the $8$ months shown above is part of a total estimated annual demand

of $9,000.$ Assuming $A=1000,h=5,P=1,100$ units per month, find the optimal EPL policy and explain

if applying it for this case could be preferred.