Amalgamated Engineering makes two kinds of gearbox - manual and automatic. There are four stages in the production of these, with details of times needed and weekly availabilities given below. The company makes a profit of £64 on each manual gearbox sold and £100 on each automatic gearbox.
(a) Find an optimal solution to the problem.
(b) The company can start making a new semiautomatic gearbox that needs 4, 4, 1 and 1 hour respectively in each manufacturing stage, and gives a profit of £80 a unit. Should they make this new gearbox?