L-O USA is a large producer of cosmetic products. At their North Little Rock production facility, they have a known, constant demand of 15,000 bottles of nail polish each month. They are able to sell their nail polish for $4 per bottle. The cost to set-up their machine to dispense nail polish is $1000, so the engineers produce batches of nail polish. Once the machine is set-up, each bottle of nail polish can be produced for $0.50. L-O estimates their holding cost to be $1.20 per bottle per year.

a) What is the optimal number of bottles to produce in each batch?

b) How often should L-O be producing a batch of Parka Perfect?

c) What is the annual profit from nail polish?

d) Suppose L-O has the opportunity to switch to a new bottling machine that only costs $750 to set-up a new nail polish color to be bottled, but it also causes the variable cost increase to $0.75. How would L-Os batch production plan change if they switched to this machine? Should L-O switch to using this new machine?