Please show all work!

Consider a POQ model with demand rate a, setup cost K, holding cost h, and production rate r. Suppose that the production process changes so that r = ? (i.e. we now have a regular EOQ model). Assume that the purchasing cost c is equal to 0.

1. If all other parameters are held constant, how much does the holding cost need to decrease in order for the optimal cost of the process to remain the same?

2. If all other parameters are held constant, how much does the ?xed cost need to decrease in order for the optimal cost of the process to remain the same?

3. Consider an EOQ model with shortages having demand rate a, setup cost K, holding cost h, and shortage cost p. Alternatively, consider a POQ model with demand rate a, setup cost K, holding cost h, and production rate r. Find an expression that describes r as a function of the other variables in order for the two processes to have the same optimal cost.