Mr$.$ Jack recently completed a course in logistics management and now realizes that there are significant costs associated with ordering and maintaining inventory at his distribution center. Mr$.$ Jack has learned that the EOQ is the replenishment logic that minimizes these costs. In an effort to find the EOQ for measuring cups, Mr$.$ Jack has gathered relevant data. Mr$.$ Jack expects to sell $50,000$ measuring cups this year. ABC Company acquires the measuring cups for $75$ cents each from XYZ Industries. XYZ charges $$8$ for processing each order. In addition, Mr$.$ Jack estimates his company$$s inventory carrying cost to be $12$ percent annually.

a$.$ Find Mr$.$ Jack EOQ for measuring cups. Assume that Mr$.$ Jack accepts ownership of products upon arrival at his DC$.$

b$.$ Now assume Mr$.$ Jack must arrange for inbound transportation of the measuring cups since ABC Company accepts ownership of products at the supplier$$s shipping point. Quantities of fewer than $4,000$ measuring cups cost $5$ cents per unit to ship. Quantities of $4,000$ and above cost $4$ cents per unit to ship. Determine the difference in total costs associated with an EOQ of $4,000$ units and the EOQ level found in part $($a$)$ when transportation costs must be considered.

c$.$ Given the information above and the low cost EOQ alternative determined in part $($b$),$ use period$-$order$-$quantity logic to determine the number of orders ABC Company would place each year for measuring cups and the time interval between orders.