Wholesale Building Materials $($WBM$)$ plans to enter Florida market during the next fiscal year. The company has already decided a product line that they will introduce to the FL market. WBM$$s plan is to serve FL from a DC located in Houston, TX$.$ As an initial market entrance strategy, WBM has signed a vendor managed inventory $($VMI$)$ contract with a company in FL$.$ According to the contract WBM needs to bring $7\%$ of the total demand during each inventory replenishment cycle $($i$.$e$.,$ shipment size is $7\%$ of the total demand$)$ in addition an amount equal to the replenishment quantity will be kept as the average inventory in Houston against contingencies. The expected demand in the market will be a function of time responsiveness of WBM$.$ The demand function is defined as follows:

D$=19700-(1430*$T$^2)/3$

Where D is demand per year in terms of normalized units and T $($in days$)$ is the response time for a certain mode of transportation. Cost of each product is $$80$ in TX$,$ inventory holding rate per unit per year is $24\%,$ transportation cost is paid to the transportation company after items are delivered to FL$,$ and sales price of each item in FL is $220($assume all units brought to FL will be sold$).$ Find what mode of transportation should be chosen to maximize the company$$s first year profit. $($Use two decimal place accuracy for cost $[$e$.$g$.,0\mathrm{.}12]$ and round shipment quantity to the nearest integer$)(30$ points$)$