Paula Perkins, the owner of Paula’s Perfume Shoppe, expects to sell 800 bottles of a certain brand of perfume this year. The perfume costs $20 per bottle, the ordering fee is $10 per shipment, and the cost of storing the perfume is 40 cents per bottle per year. The perfume is sold at a constant rate throughout the year, and each shipment arrives just as the preceding shipment is being used up.

a. How many bottles should Paula order in each shipment to minimize total cost?

b. How often should Paula order the perfume?