$1.$ 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: