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
