2 Xelia Corporation is a supplier of control systems to major avionics companies

Question

2 Xelia Corporation is a supplier of control systems to major avionics companies Demand for control systems is about 2 000 units per year The Xelia plant in Minneapolis can produce at a rate of 200 units per imonth. Each unit costs Xelia $1 produce and the setup cost for beginning a production run is $1000. Assume the company uses an arnual rate of return on investments of 25%. What is the optimal number of units to produce in each run? what is total cost? what is the util the production facility? What is the maximum dollar investment in tnished goods inventory that Kelia has at any time ie, the most value held in inventory at any timel? ery Videos

Explanation / Answer

Demand (D) = 2000

Usage rate (u) per month = 2000/12 = 166.67

production rate (p) = 200

Price = 100

Ordering cost (S) = 1000

Holding cost (H) = 25%*Price = 25%*100 = 25

Optimal level of production (Q) = sqrt(2*D*S/H)*sqrt(p/(p-u)) = sqrt(2*2000*1000/25)*sqrt(200/(200-166.67)) = 980

Utilization of production facility = usage rate/production rate = 166.67/200 = 83.3%

Maximum Inventory (I) = Q/p*(p-u) = 980/200*(200-166.67) = 163

Maximum Inventory cost = I/2*H = 163/2*25 = 2037.5 $

Total cost = D*Price + Maximum Inventory cost + D/Q*S = 2000*100 + 2037.5 + 2000/980*1000 = 204,078 $

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