An Air Force is experimenting with three types of bombs P, Q and R in which three kinds of explosives, viz. A, B and C will be used. Taking the various factors into account, it has been decided to use maximum of 600kg of explosive A, atleast 480kg of explosive B and exactly 540kg of explosive C. Bomb P requires 3, 2, 2kg, bomb Q requires 1, 4, 3kg and bomb R requires 4, 2, 3kg of explosives A, B and C respectively. Bomb P is expected to give the equivalent of a 2 ton explosion, bomb Q, a 3 ton explosion and bomb R, a 4 ton explosion respectively. Under what production schedule can the Air Force make the biggest bang? wich explosive have excess amont ans how much?

Let x, y, z be the number of bombs made of type P, Q & R respectively.

P requires: 3 kg A, 2kg B, 2kg C; Q: 1kg A, 4kg B, 3 kg C; R: 4kg A, 2kg B, 3 kg C

Explosives available:

A: max. 600kg; B: min. 480kg; …