Question

We assume that in a vilage there are tamers, cappenters, and talons, who provide the Aree essential goods: food, houting, and clothing, suppose the famers consume 2 , of the food foreduced by farneng. 1/3 of the houting (produced by carpenters) and 1/2 of the clothen (produced by talbeit the carpenter consumes 1/3 of the food, 1/3 of the houshg, and 1/2 of the ciothes The talon concume 91 of the food, 31of the houting, and no clothes. Assume this is a closed Loontet model. If we know that the talos produce 688 units of clothes, then the tarmen produce unts of food and the earpenters produce units of housing

Answer 1

The farmers produce 289.5 units of food, and the carpenters produce 723.75 units of housing.

Step-by-step explanation:

To solve the problem, we need to use the information provided and set up a system of equations. Let f, c, and t represent the units of food, housing, and clothing produced by the farmers, carpenters, and tailors respectively. We have the following equations:

f = 2c/3 + t/2

c = f/3 + h/3 + c/2

t = 91

t = 688

Substituting the values of c and t into the first equation, we get:

f = 2(688)/3 + 91/2

f = 1376/3 + 91/2

f = 916/3 + 91/2

f = 244 + 45.5

f = 289.5

Therefore, the farmers produce 289.5 units of food. To find the units of housing produced by the carpenters, we can substitute the value of f into the second equation:

h = (289.5)/3 + h/3 + (289.5)/2

h = 289.5/3 + 2h/3 + 144.75

h = 96.5 + 2h/3 + 144.75

h - 2h/3 = 96.5 + 144.75

h/3 = 241.25

h = 723.75

Therefore, the carpenters produce 723.75 units of housing.