(Show all your works: including all computational procedures and details) Assumption 1: 50 weeks in 1 year. Assumption 2: Holding costs are based on an annual interest rate of 10%. Precision Machine Company (PMC) produces computer parts labeled “PC1” for computer manufacturers. The manufacturer’s weekly demand, R, of the computer part is R = 10 parts/week. PMC has two supply options. (1) Option 1: PMC buys essential part form a Japanese supplier (unit purchasing cost = $200/unit), uses it to manufacture computer part “PC1” (unit manufacturing cost = $100/unit), and sells them to computer manufacturers. The manufacturing rate, M, of the computer part is M = 20 units/week. At the beginning of each production cycle, it costs PMC a Manufacturing Setup Cost (MSC)=$4,000 for setting up the production cycle. (Example: Assume that in each production cycle PMC produces Q=250 units of computer parts. Then, there are 2 production cycles in a year (R/Q=500/250=2); thus, PMC’s annual MSC cost is 2*$4,000=$8,000).

Figure 1 Option 1 (2)

Option 2: PMC orders (buys) the computer part “PC1” directly from the Japanese supplier and sells them to computer manufacturers (unit purchasing cost = $400/unit). At the beginning of each order cycle, it costs PMC a fix order Cost=$2,000 (i.e., it costs PMC $2,000 to initiate an order) for ordering the computer part. (Example: Assume that in each order cycle PMC orders 100 units of computer parts. Then, there are 5 order cycles in a year (500/100=5); thus, PMC’s annual order setup cost is 5*$2,000=$10,000)

Figure 2. Option 2 (a)

Option 1:

(a.1) Note that (see Figure 1) H=Q×y. Determine what is y=.

(a.2) Determine the optimal manufacturing quantity (Q) that minimizes the annual inventory cost (AIC).

(a.3) Computes AIC. AIC = Annual MSC Cost + Annual Holding Cost + Annual (purchasing + manufacturing) Cost (b)

Option 2:

(b.1) Determine the optimal inventory level (Q) that minimizes annual inventory cost (AIC).

(b.2) Computes AIC. AIC = Annual setup (order) Cost + Annual Holding Cost + Annual (purchasing) Cost

(c) PMC adopts Option 2 if the purchasing cost in Option 2 is lower than X. Computes X.

(Manufacturing Quantity) Inventory Level H manufacturing setup (maximum Inventory) M-R Time Production cle