# Question & Answer: A domestic automobile manufacturer schedules 12 two-person teams to assemble 4.6 liter DOHC V-8 engines per work day. Each team can ass…..

A domestic automobile manufacturer schedules 12 two-person teams to assemble 4.6 liter DOHC V-8 engines per work day. Each team can assemble five engines per day. The automobile final assembly line creates an annual demand for the DOHC engine at 10,080 units per year. The engine and automobile assembly plants operate six days per week, 48 weeks per year. The engine assembly line also produces SOHC V-8 engines. The cost to switch the production line from one type of engine to the other is \$100,000. It costs \$2,000 to store one DOHC V-8 for one year. a) What is the economic lot size? b) How long is the production run? c) What is the average quantity in inventory? d) What are the total annual relevant costs?

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a. Economic Lot Size Demand per day = d = 10,080/[(48)(6)] = 35

$\sqrt{2 (10,8000) (1,00,000)/2,000))}\sqrt{60/60-35}$ 

= 1555.38 = 1,555 Engines

b. The production run =    Q / P = 1,555 / 60 = 25.91 OR 26 production days

c. Average inventory

=I max / 2 = Q/2 ( p – d / p) = 1555/ 2( 60 -35 /60 ) = 324 engines

d. Total annual cost

c= I max / 2 (H) + D/Q (S) = Q/2(p-d/p)(H) +D/Q (S)

= 1555/2(60-35/60) 2,000 + 10,800/1,555 (1,00,000)

=\$647,917 + \$648,231 =\$1,296,148 