Suppose that the production of crayons   (q)   is conducted at two locations and uses only labor as an input. The production function in location 1 is given by   q_{1}=10 $l_{1}$^{0.5}   and in location 2 by   $q_{2}=50 $l_{2}$^{0.5}$  
a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations to do so? Explain precisely the relationship between   $l_{1}$   and   $l_{2}$  .
b. Assuming that the firm operates in the efficient manner described in part (a), how does total output   (q)   depend on the total amount of labor hired   (l)   ?

Suppose that the production of crayons $(q)$ is conducted at two locations and uses only labor as an input. The production function in location 1 is given by $q_{1}=10 l_{1}^{0.5}$ and in location 2 by $q_{2}=50 d_{2}^{0 .}$. a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations to do so? Explain precisely the relationship between $l_{1}$ and $l_{2}$. b. Assuming that the firm operates in the efficient manner described in part (a), how does total output $(q)$ depend on the total amount of labor hired $(l)$ ?