A firm manufactures two types of products A and B and sells them at a profit of F$2 on type A and F$3 on type B. Each product is processed on two machines ?1 and ?2. Type A requires 1 minute of processing time on ?1 and 2 minutes on ?2. Type B requires 1 minute on ?1 and 1 minute on ?2 . Machine ?1 is available for not more than 6 hours and 40 minutes while machine ?2 is available for 10 hours during a working day. Formulate the problem as an LPP so as to maximize the profit. Find the maximum profit.