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# ORIE_451_Homework_1_2008_answers - ORIE 451/551 Homework#1...

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ORIE 451/551 Homework #1 1. EEA Manufacturing estimates the following costs for various levels of production for the year. Production (units) Total Cost (\$) 14,000 \$53,400,000 20,000 \$57,960,000 26,000 \$64,050,000 a) Find the fixed annual cost and the variable cost per unit. Using linear regression the best curve fit is given by: Total Cost = \$40,720,000 + 887.50 D The fixed annual cost is \$40,720,000 (5 points) The variable cost per unit is \$887.50 (5 points) b) If annual production is 20,000 units, what selling price per unit would be needed to break even? Using the estimated cost, we would need revenue of \$57,960,000, or \$2,898 per unit. Using the curve fit, we would need F V C 40,720,000 p C 887.50 \$2,923.50 D' 20,000 = + = + = Either answer is acceptable (10 points) 2. Snakisco Inc. is looking to buy a new machine from a supplier for their manufacturing facility. Determine the ranges of annual production under which each machine would be preferred. Machine’s Supplier Annual Fixed Cost Variable Cost per Unit Adapco Enterprises \$100,000 \$20 Branson Industries \$200,000 \$5 Cobalt Incorporated \$150,000 \$7.50 0 D 4,000 Adapco (20 points) 4,000 D 20,000 Cobalt 20,000 D Branson

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3. A manufacturer has just started construction of a complicated welded assembly. The number of labor hours required for welding for each unit follow: Unit Welding Time (hours) 1 182.6 2 153.4 3 125.6 4 117.9 Find the estimated welding time for the fifth and sixth units, assuming that learning is taking place. Step 1) Take the logarithms of u and Z u Unit Log u Welding Time (hours) Log Z u 1 0 182.6 2.2615 2 0.3010 153.4 2.1858 3 0.4771 125.6 2.0990 4 0.6021 117.9 2.0715 Step 2) Using linear regression, find the slope and intercept of the Log Zu versus Log u data. Slope = - 0.3274 Intercept = 2.2674 Step 3) Find n and K n = slope = - 0.3274 K = antilog(intercept) = 10 2.2674 = 185.115 Step 4) Plug values into the equation: n u Z Ku = ( 29 ( 29 0.3274 5 Z 185.115 5 109.3 - = = hours ( 29 ( 29 0.3274 6 Z 185.115 6 103.0 - = = hours (20 points)
4. Find the unit labor cost for this industrial filter. Assume PFD = 15%. The average worker makes \$12 per hour, with additional benefit costs of 35%.

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