I am sorry I didn't explain in better details, so here is the whole problem:
This is not an exercise or homework, this is a real problem that I am trying to solve for the company I work for.
In this particular problem, we provide 4 types of services to our clients.
Service X
Service Y
Service Z
Service W
I want to know how many of each service we do daily, this is the information I have:
Time it takes to do service X = a
Time it takes to do service Y = b
Time it takes to do service Z = c
Time it takes to do service W = d
(a,b,c and d are all constants that I know)
I also know the proportion of each service in relation to the sum of all the service done daily:
Service X represents 56,4% of all services
Service Y represents 38,5% of all services
Service Z represents 3,1% of all services
Service W represents 2,0% of all services
Furthermore "e" is the time of the shift
The equations above are where I stopped. I tried solving in Wolfram Alpha but I do not know enough about the program to type these equations.
Basically I need functions as follows:
X=f(a,b,c,d,e)
Y=f(a,b,c,d,e)
Z=f(a,b,c,d,e)
W=f(a,b,c,d,e)
I need them as functions of the time of each service because i am trying to implement this in an excel spreadshet where the user can change the times.