Question

Leonard’s company purchases a window hardware from William’s Hardware Co and sells to the market. Leonard is also considering manufacturing the product internally. William’s Hardware Co. charges $4 per unit, with a minimum order of 3,000 units. If Leonard manufactures the product in-home, the process setup fee could be $15,000 and then $1.82 per unit for labor and materials.

a) Draw a graph illustrating the crossover (or indifference) point.

b) Determine the number of units where either choice has the same cost.

Answer 1

(a)

Total cost, Purchase = $4 x 3,000 + $4 x (Q - 3,000) = $12,000 + $4 x (Q - 3,000) [since minimum quantity is 3,000]

Total cost, In-house = $15,000 + $1.82 x Q

In following graph, cross-over point is point A where TC curves intersect with indifference quantity of Q*.

(b)

Equating total cost for both options,

12,000 + 4 x (Q - 3,000) = 15,000 + 1.82 x Q

4Q - 12,000 = 3,000 + 1.82Q

2.18Q = 15,000

Q = 6,881 units