In a small scale industry, a manufacturer produces two types of book cases. The first type of book case requires 3 hours on machine A and 2 hours on machine B for completion whereas the second type of book case requires 3 hours on machine A and 3 hours on machine B. The machines A and B respectively run for at the most 18 hours and 14 hours per day. He earns a profit of 30 on each type of case of first type and 40 on each book case of second type. How many book cases of each type should he manufacture so as to have maximum profit. Make it an LPP and solve it graphically.