Amanufacturer makes two types of handmade fancy paper bags: type a and type b. two designers—a cutter and a finisher—need to work on both kinds of bags. a type a bag requires 2 hours of the cutter's time and 1 hour of the finisher's time. a type b bag requires 1 hour of the cutter's time and 2 hours of the finisher's time. each month the cutter is available for 104 hours and the finisher is available for 76 hours. the manufacturer gets a profit of $6 on each bag of type a and $11 on each bag of type b. identify the number of bags of each type to be manufactured to obtain maximum profit.