A firm manufactures two types of couplings, A and B, each of which requires processing time on lathes, grinders and polishers. The machine times needed for each type of coupling are given in the table Coupling type Time required (hours) Lathe Grinder Polisher The total machine time available is 250hours on lathes, 310 hours on grinders and 160hours on polishers. The net profit per coupling of type A is $9 and of type B is S10. Formulate a linear model from the above information. Using the model, determine a) The number of each type to be produced to maximize profit
b) The maximum profit