Question

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 $10 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 $175,000 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 for annual volumes of or less, is best. for annual volumes at or above that amount, it is best to produce in house at a variable cost of $ per unit. rev: 02_09_2017_qc_cs-78259

Answer 1

For amounts over 35,000 units, in house option A is cheaper.

Find the break even quantity (aka make the equations equal) of the outside vendor compared to each in-house option.

Vendor vs in house option A:

10x = 175,000 + 5x  (subtract 5x from both sides)

5x = 175,000 (divide by 5)

x = 35,000 units

vendor is cheaper than option A up to 35,000 units

Vendor vs. in-house option B

10x = 190,000 + 4x (subtract 4x from both sides)

6x = 190,000 (divide by 6)

x = 31,667 (rounded to nearest unit)

vendor is cheaper than option B up to 31,667 units