Mr. Kugi, the owner and manager of the Quality Hardware Store, is reassessing his inventory policy for hammers. He sells an average of 50 hammers per month, so he has been placing an order to purchase 50 hammers from a wholesaler at a cost of P20 per hammer at the end of each month. However, Mr. Kugi does all the ordering for the store himself and finds that this is taking a great deal of his time. He estimates that the value of his time spent in placing each order for hammers is P75.

a)What would the unit holding cost for hammers need to be for Mr. Kugi's current inventory policy to be optimal according to the basic EOQ model? What is this unit holding cost as a percentage of the unit acquisition cost?

b)What is the optimal order quantity if the unit holding cost actually is 20 percent of the unit acquisition cost?What is the corresponding value of the total variable inventory cost (TVC) or holding costs plus the administrative costs for placing orders per year)?

c)If the wholesaler typically delivers an order of hammers in 5 working days (out of 25 working days in an average month), what should the reorder point be?

d)Mr. Kugi doesn't like to incur inventory shortages of important items. Therefore, he has decided to add a safety stock of 5 hammers to safeguard against late deliveries and larger-than-usual sales. What is his new reorder point? How much does this safety stock add to TVC?

A factory situated along the River Ganges discharges two types of pollutants from its tanning and dyeing manufacturing processes into the river. To remove the pollutants from its effluents, the factory installed "minimum discharge" technology, which costs $25 and $10 to process a ton of tanning wastes and a ton of dyeing wastes respectively. The technology removes 0.1 tons of pollutant 1 from a ton of tanning waste and removes 0.2 tons of it from a ton of dyeing waste. In the case of pollutant 2, it removes 0.3 tons of dyeing waste and 0.08 tons of tanning waste from every ton of each of the wastes processed. Since tanning wastes are more harmful than dyeing wastes, the factory plans to process more tanning wastes than dyeing wastes. The current policy is that the tons of tanning waste processed is at least twice as much as the tons of dyeing waste processed. The factory has to remove at least 25 tons of pollutant 1 and at least 35 tons of pollutant 2. Formulate a linear programming problem to minimize cost.