sorry for bad formatting earlier
We are given Cx,i, Cy,i, Cz,i ∈ ℕ and Px,i, Py,i, Pz,i > 0 for i=1,2,3 such that Px,1 < Px,2 < Px,3, Py,1 < Py,2 < Py,3, and Pz,1 < Pz,2 < Pz,3. We are also given K∈ℕ.
The values Cx,i and Px,i describe the content of a stack named x. From top to bottom, the stack x contains Cx,1 items each of profit Px,1, Cx,2 items each of profit Px,2, and Cx,3 items each of profit Px,3. The contents of stacks y and z are defined in the same way.
We are allowed to pop K items in total from the three stacks. How can I maximize the total profit?