A certain economy contains three industries: art, education, and gardening and their economic output is measured in units of fulfilment (e.g. 1 unit of fulfilment is equivalent to seeing someone smile.) 20% of the economic output of art goes back to art, 40% goes to education, and 10% to gardening. Also, for every unit of fulfilment generated from education, .1 goes art, .4 goes to education, and none to gardening. Of every 100 units of fulfilment generated by gardening, art consumes 30 and education 20 while gardening consumes none. In addition, there is an external demand of 42000 units of fulfilment of art, 84000 of education, and 12600 of gardening. a. Write the input-output matrix and demand vector for this open Leontief model. b. How much should each industry produce in order to meet demand?