Answer:
You require 10 helpers 
Step-by-step explanation:
The problem could be solved in many ways ( like using an optimization software) but I propose you this. 
Start with production of large cakes.  In the time kitchen is available one helper could make, if only works in large cakes: 
(2 large cakes / 1 hour) * (3 hours ) = 6 large cakes 
So with 3 helpers using all their 3 hours we would have
 3 helpers *6 large cakes /helper  = 18 large cakes. 
We need 2 more large cakes so we can use one more helper and in his first hour he can produce 
(2 large cakes / 1 hour) * (1 hour ) = 2 large cakes 
The 4th helper has two hours of work left so he can produce small cakes. 
(35 small cakes/hour* 2 hours = 70 small cakes. 
With 4 helpers we have the 20 large cakes and 70 small ones. We still have to makes 
700 - 70 = 630 small cakes left 
In the 3 hour period a helper can make 
(35 small cakes / 1 hour) * (3 hours ) = 105 large cakes 
So if 1 helper does  105 large cakes  we would need to finish production with 
630 / 105 =  6 helpers
So in total we have 3 helpers in only large cakes 6 in only small cakes and one helper doing both - total 10 helpers