Question

A firm plans to begin production of a new small appliance. The manager has three options:

Option 1: purchase the motors for the appliance from a vendor at $9 each

Option 2: produce them in house using technology A with an annual fixed cost of $40000 and a variable cost of $4 per unit

Option 3: produce them in house using technology B with an annual fixed cost of $125000 and a variable cost of $3 per unit

The range of output for which option 1 is best is ________ units

The range of output for which option 2 is best is ________units

The range of output for which option 3 is best is ________units

Answer 1

The range of output for which option 1 is best is 0 to 8000 units

The range of output for which option 2 is best is 8000 to 20833 units

The range of output for which option 3 is best is more than 20833 units

Explanation:

n be the number of units.

At the break-even point, total cost for making = total cost for buying

cost for motor while buying using option 1 = $9*n

Cost for producing the motors using option 2 = fixed cost + variable cost = 40000+($4)n

The condition for break-even is

9n = 40000+4n

5n = 40000

n= 8000 units

Hence at volume of 8000, the firm would be indifferent between making and buying and for volume lower than 8000 the choice would be to buy using option 1 and for volume higher than 8000, the choice would be to make in house using option 2.

Total Cost for producing using option 3 =125000 + (3*n)

At break-even point, 9n = 125000 + 3n

6n = 125000

n = 20833.33 = 20833 motors

Hence the option 2 would be feasible only if the volume is higher than 20833.