ORIE_350_Homework__9_Solutions

ORIE_350_Homework__9_Solutions - ORIE 350 Homework#9...

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ORIE 350 Homework #9 Solutions 1. If the first FSAE car built took 400 assembly hours, and the doubling parameter had value 0.80, how long did it take the FSAE team to assemble the 10 th car? Given: s = 0.80 K = 400 hours Calculations: logs log0.80 0.09691 n 0.032193 log 2 log 2 0.3010 - = = = = - n u Z Ku = We want the value of Z for the 10 th car, so u = 10 and ( 29 0.0321928 10 Z 400 10 190.6 - = = It takes 190.6 hours to assemble the 10 th car. 2. A contractor manufactures large backup power systems . Given the following data, estimate the cost of units 5, 6, and 7. Unit 1: $7,815,000 Unit 2: $7,424,000 Unit 3: $7,205,000 Unit 4: $7,053,000 Step 1: Take the logs of both u and Z u Z log u log Z 1 7,815,000 0 6.89293 2 7,424,000 0.3010 6.87064 3 7,205,000 0.4771 6.85763 4 7,053,000 0.6021 6.84837
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Next, we see that using the log form of the learning equation, we get a straight line: u log Z log K n log u = + with log K = intercept n = slope Plotting log Z versus log u, we obtain: 6.74 6.76 6.78 6.8 6.82 6.84 6.86 6.88 6.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 We see the intercept is 6.89293, so solve for K 6.89293 log K 6.89293 K 10 7,815,018 = = = Measuring the slope, we find it is - 0.074, so n = - 0.074 Then we are ready to calculate Z 5 , Z 6, and Z 7 . . ( 29 ( 29 ( 29 0.074 5 0.074 6 0.074 7 Z 7,815,018 5 $6,937,551 Z 7,815,018 6 $6,844,580 Z 7,815,018 7 $6,766,946 - - - = = = = = =
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3.27 (ABC versus traditional costing.) a. Using the Three Cost Drivers High Rate Standard Grade Total Direct Materials .................... $       125,000     a $       114,000     $              239,000     Direct Labor ........................... $       160,000     b $             80,000     $              240,000     Overhead Costs: Number of Production  Runs ................................ $ 10,000 c $ 200,000 f $ 100,000 $ 300,000  Number of Quality  Tests ................................ 12,000 d 144,000 g 216,000 360,000 Number of Shipping  Orders ............................. 1,466.67 e 146,667 h            73,333                 220,000     Total Overhead ...................... $       490,667     $       389,333     $              880,000     Total Costs ............................. $       775,667     $       583,333     $        1,359,000     Total Unit Cost ...................... $2.42 i $4.86 i a Data given in the text. b Data given in the text. c $10,000 per run = $300,000 in production costs/30 total runs. d $12,000 per test = $360,000 in quality costs/30 total tests. e $1,466.67 per order = $220,000 in shipping costs/150 shipping orders. f $200,000 = $10,000 per production run  X  20 runs for Standard. g $144,000 = $12,000 per quality test  X  12 tests for Standard.
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