A leather shop makes custom-designed, hand-tooled briefcases and luggage. The shop makes a $400 profit from each briefcase and a $200 profit from each piece of luggage. (The profit for briefcase is higher because briefcases require more hand-tooling.) The shop has a contract to provide a store up to 30 items per month. A tannery supplies the shop with at least 80 square yards of leather per month. The shop must purchase at least this amount but can order more. Each brief case requires 2 square yards of leather; each piece of luggage requires 8 square yards of leather. From the past performance, the shop owners know they cannot make more than 20 briefcases per month. They want to know the number of briefcases and pieces of luggage to produce in order to maximize profit. Formulate a LP model for this problem.