$($Factory Physics, Chapter $2$ Problem $9)$ Nozone, Inc., a manufacturer of Freon recovery units

$($for automotive air conditioner maintenance$),$ experiences a strongly seasonal demand patter,

driven by the summer air conditioning season. This year Nozone has put together a $6-$month

production plan, where the monthly demands $D_t$ for recovery units are given in the table

below. Each recovery unit is manufactured from one chassis assembly plus a variety of other

parts. The chassis assemblies are produced in the machining center. Since there is a single

chassis assembly per recovery unit, the demands in the table below also represent the demands

for the chassis assemblies. The unit cost, fixed setup cost, and the monthly holding cost for

chassis assemblies are also given in this table. The fixed setup cost is the firm's estimate of

the cost to change over the machining center to produce chassis assemblies, including labor

and materials cost and the cost of disruption of other product lines.

$($a$)$ Formulate the problem of production scheduling for chassis assemblies as an MILP.

$($b$)$ Formulate the above problem as a shortest $($least costly$)$ path problem. In particular,

draw the corresponding network and compute the various edge costs.

$($c$)$ Solve the above shortest path problem. $($You may find it less cumbersome to compute

edge costs and the optimal solution if you use Excel, Python, etc.$)$