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 for $6.70 each or to produce them in house. There are two in house options.

Option 1 would have an annual fixed cost of $161000 and a variable cost of $5.90.

Option 2 would have an annual fixed cost of $194000 and a variable cost of $4.10.

Calculate the maximum quantity that would have the manager select purchasing the motors from the vendor.

Answer 1

Total cost for purchasing option, TC(P) = 6.70*Q
Total cost for option-1, TC(1) = 161000 + 5.90*Q
Total cost for option-1, TC(2) = 194000 + 4.10*Q

Cross-over point between Purchase and Option-2

= [Fixed cost of Option-2 - Fixed cost of Purchase] / [Variable cost of Purchase - Variable cost of Option-2]

= (194000 - 0) / (6.7 - 4.1)

= 74615.38

So,

The purchasing option is the best only up to a maximum quantity of Q = 74615