A manufacturer produces two models of racing bike, B and C, each of which must be processed through two machine shops. Machine shop 1 is available for 120 hours per month and machine shop 2 for 180 hours per month. The manufacture of each bike of type B takes six hours in shop 1 and three hours in shop 2. The corresponding times for C are 4 and 10 hours, respectively. If the profit is $180 and $220 per bike of type B and C, respectively, how should the manufacturer arrange production to maximise total profit?