A Bike Company has a line of specialty mountain bikes which

A Bike Company has a line of specialty mountain bikes which require 5,000 handlebars annually. The handlebars can be purchased from a supplier for $30 per unit, or they can be produced internally. The internal production cost is $20 per unit, and the production rate is 20,000 units per year. The cost to set up production is $5000. It costs $25 to issue a purchase order to buy handlebars from the supplier. Inventory holding cost is 25% per year.
a. If the Bike Company decides to purchase the handlebars, what is the optimal order quantity? What is the annual cost?

b. If the Bike Company decides to produce the handlebars, what is the optimal order quantity? What is the annual cost?

Solution

a) Q = optimal order quantity = sqrt(2*D*k/h)

k = cost per order = 25

D = annual demand =5000

P = Purchase price = 30

h = holding cost= 25%*30 = 7.5

Q = sqrt(2*5000*25/7.5) = 193

TC = 30*5000 + 5000*25/183 + 7.5*183/2 = $151369.3

b. to answer this part the annual fixed cost for production is laso needed