Question

Dusty is evaluating two bids to supply fence hardware for the 5 acres of pasture that need to be fenced. Breezy submits a bid of​ $40 per unit with a defect rate of​ 3%; Lady's bid is​ $50 per unit and their product manager estimates the defect rate to be around​ 0.5%. If a section of fence​ fails, it costs an average of​ $500 in losses and herding costs to round up all of the capybaras. Dusty believes it will take 500 units to fence in this pasture configuration. The product​ manager's uncertainty has Dusty​ concerned; what defect rate for Lady would make Dusty indifferent between the two suppliers as far as total cost is​ concerned?

Answer 1

Solution:

Cost of fence from breezy = $40*500 = $20,000

Defect rate of Breezy = 3%

Estimated defect in 500 units = 500*3% = 15 units

Cost of herding if defect occurs = 15*500 = $7500

Net cost of breezy fence = $20,000 + $7,500 = $27,500

Cost of fence from lady = $50*500 = $25,000

Defect rate of lady fence = 0.5%

expected defect = $500*0.5% = 2.50 units

Cost of herding if defect occurs = 2.5*500 = $1250

Net cost of breezy fence = $25,000 + $1,250 = $26,250

Now dusty will be indifferent between two suppliers if cost including defect under both supplier will be same i.e. $27,500

In order for net cost of Lady's equal to $27,500, required defect cost = $27,500 - $25,000 = $2,500

Required number of defect = $2,500 / 500 = 5 defect

Defect rate for lady that make dusty indifferent between two supplier = 5/500 = 1%