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Department of MathematicsMATH1003TUTORIAL 2 : Week 41. A Furniture Factory has 1950 machine hours available each week in the cutting de-partment, 1490 hours in the assembly department, and 2160 hours in the finishingdepartment.•Manufacturing a chair requires 0.2 hours of cutting, 0.3 hours of assembly, and0.1 hours of finishing;•Manufacturing a cabinet requires 0.5 hours of cutting, 0.4 hours of assembly, and0.6 hours of finishing;•Manufacturing a buffet requires 0.3 hours of cutting, 0.1 hours of assembly, and0.4 hours of finishing.(1) Write the linear system which describes the manufacture of chairs, cabinets andbuffets.Do not solve.(2) Write the associated augmented matrix.2. Use row operations to find a value forhsuch that the following matrix is the augmentedmatrix of a consistent linear system.(a)11-1-1h-3;(b)47-8h-37.3. Use row reduction on the augmented matrix to solve the following linear systems:(a)2x1-4x2=14x1-5x2=-33x1-6x2=2(b)-3x+ 2y-6z=65x+ 7y-5z=6x+ 4y-2z=8(c)