A firm produces by means of two raw materials R1 and R2 three intermediate products S1, S2 and S3, and with these intermediate products two final products F1 and F2. The numbers of units of R1 and R2 necessary for the production of 1 unit of Sj, j ∈ {1, 2, 3}, and the numbers of units of S1, S2 and S3 necessary to produce 1 unit of F1 and F2, are given in the following tables:

 

Solve the following problems by means of matrix operations.

(a) How many raw materials are required when 1,000 units of F1 and 2,000 units of F2 have to be produced?

(b) The costs for one unit of raw material are 3 EUR for R1 and 5 EUR for R2. Calculate the costs for intermediate and final products.

S S2 S3 3 R 2 5 R 5 4 1 F F2 60 S $ 1 S3 3 4 2