An Input-Output Model for a Three-Sector Economy Consider a simple economy consisting of three sectors: food, clothing, and shelter. The production of 1 unit of food requires the consumption of 0.4 unit of food, 0.2 unit of clothing, and 0.2 unit of shelter. The production of 1 unit of clothing requires the consumption of 0.1 unit of food, 0.2 unit of clothing, and 0.3 unit of shelter. The production of 1 unit of shelter requires the consumption of 0.3 unit of food, 0.1 unit of clothing, and 0.1 unit of shelter. Find the level of production for each sector to satisfy the demand for 100 million worth of food, 30 million worth of clothing, and 250 million worth of shelter.
a) Food: 400 units, Clothing: 200 units, Shelter: 200 units
b) Food: 300 units, Clothing: 200 units, Shelter: 300 units
c) Food: 200 units, Clothing: 200 units, Shelter: 400 units
d) Food: 200 units, Clothing: 300 units, Shelter: 300 units