A firm plans to begin production of a new small appliance. The manager must deci

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 $7 each or to produce them in-house. Either of two processes could be used for in-house production; one would have an annual fixed cost of $168,652 and a variable cost of $5 per unit, and the other would have an annual fixed cost of $192,109 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 answer to the nearest whole number.)

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; one would have an annual fixed cost of $168,652 and a variable cost of $5 per unit, and the other would have an annual fixed cost of $192,109 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 answer to the nearest whole number.)

Explanation / Answer

compare pairs to find volumes where costs are equal

firstly equate 7x = 168652+ 5x, 2x = 168652, x = 84326

then equate 168652 + 5y = 192109 + 4y, y = 26,457

finally, equate the 1st & 3rd, 7z = 192109 + 4z, z = 64,036.333

interpretation
----------------
upto volume of 64,036, purchase
for volume above 64,036 , go for option with variable cost of $4/unit

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