Linear Programming problem

Question

A cake company makes n different cakes, C1.....,Cn .
For all of its cake, the company uses a set of m ingredients,Q1......Qm .
The company has a limited amount of each ingredient available each day. Each of the cakes is made from specified quantities of the ingredients Q1......Qm per unit.
Each of the cakes is made in v stages, S1......Sv . The machine used for each stage can run for a limited number of hours each day. Manufacture of each of the cakes requires specified amounts of time in each of the stages S1......Sv per unit.
The profit made from the sale of one unit of cake Ci is P1.....,Pn , and the company wants to maximise the profit from its daily cake production.

a) Formulate this problem as a Linear Programming problem, defining all terms that you use

b) Now assume that, for each cake C1.....,Cn , there is an additional daily fixed cost Zi if cake Ci is made. Fixed cost Zi is not incurred if cake Ci is not made.
Modify your formulation to take these fixed costs into account

I'm currently struggling with part A, I seem to be okay with problems that are defined with numbers but not this.

My current thinking is

Let aij be the number of cakes Ci going through stages Sj

Maximize profit = ^(n)Σi=1 Ci.Pi

Subject to

^(m)Σi=1^(v)Σj=1 aij <=T (T is total time)

and

Something about the amount of ingredients used must be less than total ingredients?

Hoping I'm along the right lines but really struggling between the interaction of stages/ingredients/cakes and how time is placed as a restriction.