The information in this paragraph applies to this question and the $5$ questions that follow $($so$,$ questions $1-6).$

The daily demand for the Savonera bar soap, one of the luxury brands manufactured by Mellow Cosmetics Company, is $146$ soap bars.

The cost of a single soap bar is $$2\mathrm{.}50.$

The rate of holding cost per unit per day, which includes opportunity cost of investment and deterioration of a soap bar when in storage, is $1\%$ of the cost of the soap bar.

The cost of setting up machinery for making a batch of the Savonera soap bar, which includes changing the materials and tools, and wastage of initial test quantities, is $$46$ per setup. Note that setting up cost is equivalent to the ordering cost.

The company currently uses an arbitrary batch size of $6,000$ for making Savonera bars of soap. Based on this batch size and the information provided earlier, $1.$calculate and report the daily inventory holding $($carrying$)$ cost for Mellow Cosmetics Company. $2.$Based on the arbitrary batch size of $6,000$ bars of Savonera soap and the information provided earlier, please calculate and report the total daily cost of setups $($ordering$)$ for Mellow Cosmetics Company. $3.$The management of Mellow Cosmetics Company has requested your help for systematically figuring out the batch size for Savonera soap to replace their arbitrary batch size. Based on the demand and costs information provided earlier, please help by calculating and reporting the Economic Order Quantity $($EOQ$)$ for the batch size that you would recommend for manufacturing Savonera soap bars. $4.$Using the EOQ batch size that you calculated for Savonera bars of soap, please calculate and report the daily inventory holding $($carrying$)$ cost for Mellow Cosmetics Company. $5.$Using the EOQ batch size that you calculated for Savonera bars of soap, please calculate and report the total daily cost of setups $($ordering$)$ for Mellow Cosmetics Company. $6.$Compare the total daily cost of inventory management $($holding $+$ setup cost$)$ for the two quantities $(6,000$ and the EOQ you calculated$),$ i$.$e$.,$ calculate and report the difference in the total daily costs of inventory management using the two different quantities.