Two or more essences out of a stock five essences-- L, M, N, O, and P are used in making all perfumes by a manufacturer. He has learned that for a blend of essences to be agreeable it should comply with all the rules listed below.
A perfume containing L, should also contain the essence N, and the quantity of N should be twice as that of L.
A perfume containing M, must also have O as one of its components and they should be in equal proportion.
A single perfume should never contain N as well as O.
O and P should not be used together.
A perfume containing the essence P should contain P in such a proportion that the total amount of P present should be greater than the total amount of the other essence or essences used.
Among the below mentioned formulas, which can be made agreeable by the eliminating some or all of one essence ?
