$(6$ points$).$ This problem is based on the specific factors model. Consider the economy of the Shire that

produces cereals and swords. Each industry employs Hobbits, but land is specific to the production of

cereals, and metal is a specific factor in the sword industry. The amounts of land $($L$)$ and metal $($M$)$ are

L$=1000$ and M$=40,$ and there are $100$ Hobbits in Shire. The production functions and the marginal products

of Hobbits' labor are as follows: