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A firm plans to begin production of a new small appliance. The manager must decide whether to purchase the motors for the appliance from a vendor at $7 each or to produce them in-house. Either of two processes could be used for in-house production; Process A would have an annual fixed cost of $160,000 and a variable cost of $5 per unit, and Process B would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of the alternatives would be best. (Round your first answer to the nearest whole number. Include the indifference value itself in this answer.) For annual volumes of or less, is best. For annual volumes above that amount, is best.

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MsTeel

Find break even point where x=number of motors

Process A:

7x = $160,000 + 5x

2x= 160, 000

x= 80,000

For process A, the vendor is cheaper up to 80,000 motors

Process B:

7x= $190,000 + 4x

3x=190000

x= 63,333 (rounded)

For process B, the vendor is cheaper up to 63,333 motors

The vendor is cheaper up to 80000 motors and 63333 motors for processes A and B respectively.

Based on the information given, the equation to solve the question will be:

Process A:

(7 × x) = 160000 + (5 × x)

7x + 160000 + 5x

Collect like terms

7x - 5x = 160000

2x = 160000

x= 16000/2

x = 80000

Process B:

(7 × x) = 190000 + (4 × x)

7x + 190000 + 4x

Collect like terms

7x - 4x = 190000

3x = 190000

x= 19000/3

x = 63333

Therefore, the vendor is cheaper up to 80000 motors and 63333 motors for process A and B respectively.

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