Question

Audi Motors is considering three sites A, B, and at which to locate a factory to build its new model automobile, the Audi SUV XL500. The goal is to locate at a minimum-cost site, where cost is measured by the annual fixed plus variable costs of production Audi Motors has gathered the following data. Site Annualized Fixed Cost A $10,000,000 $20,000,000 $25,000,000 Variable Cost per Auto Produced $2,500 $2.000 $1,000 The firm knows it will produce between 0 and 60,000 SUV XL500s at the new plant each year, but, thus far, that is the extent of its knowledge about production plans. a) The value of volume, V. of production above which site C is recommended SUV XL500s. (Round your response up to the next whole number.) b) The value of volume, V. of production below which site A is recommended SUV XL500s. (Round your response up to the next whole number.) c) Over what range of volume is site B optimal? O A. Site B is always optimal because its cost line is always below that of A and C for all volume levels O B. Site B is optimal for volumes above 20,000 SUV XL500s. OC. Site B is optimal for volumes from 10,000 to 20,000 SUV XL 500s. OD. Site B is never optimal because its cost line always exceeds that of A or C for all volume levels.

Answer 1

Since the fixed cost of site A is least, for lower volumes, Site A is preferred.. Let X be the volume when site B OR C becomes profitable

At breakeven point with Site B, 10 million + 2500*X = 20 million + 2000*X

implies 500X = 10 million which implies X = 20,000 units

Similarly Breakeven for site C with Site A

10 milion + 2500X = 25 million + 1000X

implies, 1500X = 15 million which implies, X = 10,000 units

When we compare Site B and Site C

20 million + 2000X = 25 million + 1000X

implies 1000X = 5 million which implies, X = 5000 units This means C is better if production is more than 5000 units provided A is NOT there.

Combining all these results we would prefer Site A upto 10,000 units and post that site C. This is also confirmed with the following graph. At 10,000 units point and after that, purple line (site 3) has the lowest cost.

Audi Plant Decision per car Site Fixed Cost Variable cost А $ 10,000,000 $ 2,500 B $ 20,000,000 $ 2,000 $ 25,000,000 $ 1,000 180000000 160000000 140000000 120000000 Number of units 100000000 - Site A total cost 80000000 Site B total cost Number o Site A total cost Site B total cost Site C total cost 5000 $ 22,500,000 $ 30,000,000 $30,000,000 10000 $ 35,000,000 $ 40,000,000 $35,000,000 15000 $ 47,500,000 $ 50,000,000 $40,000,000 20000 $ 60,000,000 $ 60,000,000 $45,000,000 25000 $ 72,500,000 $ 70,000,000 $50,000,000 30000 $ 85,000,000 $80,000,000 $55,000,000 35000 $ 97,500,000 $90,000,000 $60,000,000 40000 $ 110,000,000 $100,000,000 $ 65,000,000 45000 $ 122,500,000 $110,000,000 $70,000,000 50000 $135,000,000 $ 120,000,000 $75,000,000 55000 $ 147,500,000 $ 130,000,000 $80,000,000 60000 $ 160,000,000 $ 140,000,000 $ 85,000,000 60000000 * Site C total cost 40000000 20000000 OT 1 2 3 4 5 6 7 8 9 10 11 12

b) Less than 10,000 units indicates site A is optimal.

C) Site B is not recommended for any range. As we see from graph and other calculations, at any point of time, either site A or site C has lower total cost than site B. So Site B is NOT suited for any number of volume production.