Question

Peter Billington​ Stereo, Inc., supplies car radios to auto manufacturers and is going to open a new plant. The company is undecided between Detroit and Dallas as the site. The fixed costs in Dallas are lower due to cheaper land​ costs, but the variable costs in Dallas are higher because shipping distances would increase. Dallas Detroit Fixed costs $ 560 comma 000 $ 780 comma 000 Variable costs $ 30​/radio $ 22​/radio
​a) Based on the analysis of the​ volume, after rounding the numbers to the nearest whole​ number, Dallas is best below and Detroit is best above ▼ radios. ​
b) Dallas​'s fixed costs have increased by​ 10%. Based on the analysis of the​ volume, after rounding the numbers to the nearest whole​ number, Dallas is best below and Detroit is best above ▼ 27,500 7,000 24,600 76,996 20,500 radios.

Answer 1

Answer: a) below 27,500 units Dallas is best. Above, Detroit is best.

b) below 20,500 units Dallas is best. Above, Detroit is best.

Explanation:

To calculate we shall be using the Point of Indifference Value.

Now, let's borrow x from Algebra and denote it as the Quantity (Q) where the cost of the 2 processes are equal..

a) Total cost = Fixed Costs + ( Variable cost * Q)

Dallas Total Cost = 560,000 + 30x

Detroit Total Cost = 780,000 + 22x

Equating them we get,

560,000 + 30x = 780,000 + 22x

8x = 220,000

x = 27,500 units.

Below 27,500 radio units then Dallas would be preferable due to lower fixed costs. Above 27,500 radio though then Detroit would be better due to lower Variable costs.

b) Dallas costs rise by 10%

= 560,000(1 + 0.1)

= $616,000 is their new cost.

Using the same methodology as A above we say,

616,000 + 30x = 780,000 + 22x

8x = 164,000

x = 20,500 units.

Below 20,500 radio units then Dallas would be preferable due to lower fixed costs. Above 20,500 radio though then Detroit would be better due to lower Variable costs.

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