You are given an economy with three sectors only, namely; Service (S), industry (I) and agriculture (A). The service sector uses 30 ngwee of its own output and 50 ngwee of industry output to produce a kwacha worth of output. The industry needs 20 ngwee from the service sector, 30 ngwee of its own output and 40 ngwee from agriculture to produce a kwacha worth of output. The agriculture needs 40 ngwee of service sector, 20 ngwee from the industry and 20 ngwee of its own output to produce a kwacha worth of output. The open sector demands K SOO worth of output from the service sector and Kl 000 worth of agriculture output.a.Write out:i. the input matrix ii. the Leontief matrix iii. the specific input-output matrix equation for this economyb.Obtain the gross output vector it will be necessary to produce in order to meet the open sector demand.c.If the production of one unit of the first good requires 4 hours of labour time, one unit of the second good requires 3 hours of labour time, and one unit of the third good requires 2 unit of labour time, approximately how many hours of labour time are needed to meet the vector of final demands?