$(50$ points$)$ Oz Inc. produces coffee tables in its plants in Raleigh and Houston that must be shipped to their distribution centers $($DCs$)$ in New Jersey and San Diego. The tables are distributed to the local retailers through these DCs$.$ Oz Inc. uses a $3$PL $($Third Party Logistics$)$ company to make the shipments. Suppose, through the $3$PL$,$ Oz Inc. can ship either directly to their DCs or through the DCs of the $3$PL company located in Detroit and Salt Lake City. The monthly production capacity at the Raleigh and Houston plants are $4,600$ and $6,500$ units, respectively, and the demands at the New Jersey and San Diego retailers are forecasted at $5,600$ and $3,500$ units, respectively. The cost of shipping per unit is given in the following table:FROM $/$ TO New Jersey San Diego Detroit Salt Lake CityRaleigh $ $4\mathrm{.}00$ $ $7\mathrm{.}20$ $ $3\mathrm{.}50$ $ $2\mathrm{.}90$ Houston $ $4\mathrm{.}50$ $ $2\mathrm{.}50$ $ $2\mathrm{.}00$ $ $2\mathrm{.}00$ Detroit $ $1\mathrm{.}50$ $ $5\mathrm{.}60$ $ $-$ $ $3\mathrm{.}60$ Salt Lake City $ $5\mathrm{.}00$ $ $1\mathrm{.}00$ $ $3\mathrm{.}60$ $ $-$ Identify the best shipping routes and cost by applying thea$)(10$ points$)$ Least Stage Cost Heuristic $($see lecture slides$)$b$)(10$ points$)$ Total Landed Cost Heuristic $($see lecture slides$)$c$)(10$ points$)$ Linear Programmingd$)(10$ points$)$ How do the results from parts $($a$),($b$)$ and $($c$)$ compare?e$)(10$ points$)$ There is an alternate $3$PL company indicating that they would provide the same pricing except for the Raleigh New Jersey shipment cost would be lower at $$1\mathrm{.}90/$unit but Houston to Detroit would be higher at $$3\mathrm{.}30/$unit$.$ Which career would you choose? Why? How much cost would you be saving or adding if you would switch careers? $($Base your answer on the LP Solution$)$