Solve the following problems:
I. 30 people gather, including men, women and children. It is known that men and women double the number of children. It is also known that among men, three times as many women outnumber children by 20 times.
Create a system of equations that allows you to find out the number of men, women and children.
Write the augmented matrix of the system.
Solve the proposed system of equations using the Gauss Jordan method.
ll. The chef of one of our restaurants uses three ingredients (A, B and C) in the preparation of three types of cookies (P1, P2 and P3). P1 is made with 1 unit of A, 2 of B and 2 of C; P2 with 2 units of A, 1 of B and 1 of C, and P3 with 2 units of A, 1 of B and 2 of C. The selling price is $7.2 for P1, $6.15 for P2 and $7.35 for P3. Knowing that the commercial margin (profit) is $2.4 in each of them, how much does each unit of A, B and C cost the chef?
Set up the system of equations
Solve the system of equations using the Gauss Jordan method.
III. Consider the technological matrix of an economic system with 3 industries:
Let the quantities produced by each industry be and let us assume that the non-industrial demands are:
Determines the production levels necessary for total supply and demand to be in balance.