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$\text{'}$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:

$D=19700-\frac{1430**T^2}{3}$

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$)$