Case 1. (Make necessary assumptions and solve the following questions. Show all your works: including all computational procedures and details.)

MBPF Inc. produces and sells mobile warehouses to consumers. MBPFs production process consists of recurring and identical production/demand cycles. The consumer demand of mobile warehouse during a typical production/demand cycle is 600,000 units. During the first 12 weeks of a production/demand cycle, MBPF buys two essential parts (roof and base) form a part supplier, assembles them to a finished product (i.e., mobile warehouse), and sells it to consumers. Unit manufacturing cost is $100. In each week, approximately 50,000 pairs of roof/base parts are supplied by the part supplier (thus, 12 weeks total supply = 50,000 12weeks=600,000). Moreover, it costs MBPF a Fix Transportation Cost (FTC) =$800,000 (independent of the transportation batch size) each time a batch of 50,000 parts are delivered form the suppliers warehouse to the MBPFs production facility (thus, 1 production/demand cycle Total FTC =12weeks * $800,000). Assembly of a mobile warehouse is currently performed by three resources: Machine 1, Machine 2, and Assembly Machine (AM). Machine 1 prepares part Roof (involves activities R1, R2, R3) and Machine 2 prepares part Base (Activities B1 and B2). MBPF has 1,000 units of Machine 1 and 1,200 units of Machine 2. Finally, these two parts will be assembled by AM. MBPF has 1,200 units of AM. Assume that each resource of MBPF works 40 hours (scheduled availability) per week. Activity times (minutes) and visit are summarized in the following tables.

MACHINE 1 (1000 units)	Activity Time (minutes)	Visit
R1	10	1
R2	40	1
R3	10	1

MACHINE 2 (1200 units)	Activity Time (minutes)	Visit
B1	20	1
B2	20	1

AM (1200 units)	Activity Time (minutes)	Visit
Assembly	45	1

If the inflows (part supply) exceed outflows (production/assembly) inventory will build up. An inventory unit will cost the company Unit Inventory Cost=$5 per week (For example, If MBPF keeps 2 units of inventory for 3 weeks, then the Inventory Cost = 2units3weeks$5). Moreover, MBPFs production policy specifies that all input parts during a production cycle must be processed before end of the cycle, accordingly the company begins with an empty part storeroom.

(a) Evaluate the production process and determine the Total Cost Per Cycle (TCPC). Note that

TCPC = Total FTC + Inventory Cost + Manufacturing Cost

12weeks * $800,000+2units3weeks$5+600,000=10,200,030

(b) MBPF has modified its production process so that weekly supply rate of parts is increased from 50,000/week to 100,000/week. Note that the supplier supply parts in the first 6 weeks in the modified production process so that the total supply is still 600,000 units.

(b.1) MBPF will adopt the modified production process if an FTC is higher or lower than $X (assuming other costs remain the same). Determine X. Explain why?

(b.2) MBPF will adopt the modified production process if the Unit Inventory Cost is higher or lower than $X (assuming other costs remain the same). Determine X. Explain why?