MATH 121 DISCUSSION WEEK 5 WORKSHEET 1) Consider the below matrix. A = 1 3 50 1 5 2 4 1 (a) Find A-1 . (b) How do we know that we found the correct A-1 in part (a)? (c) Using A-1 , solve the following system of equations: x + 3 y + 5 z =-7 y + 5 z = 2 2 x + 4 y + z = 3 2) Consider the below system of inequalities: 8 x + 3 y ≥ 24 2 x + 3 y ≤ 12 y ≥ 1 (a) How many boundary points and boundary lines does the feasible region of this system have? (b) Determine if the point ( 5 2 , 10 3 ) is in the feasible region. (c) Minimize the objective function 7 x + 3 y subject to the constraints given in the system of inequalities. At what exact point is this objective function minimized? (d) Maximize the objective function 5 x + 9 y subject to the constraints given in the system of inequalities. At what exact point is this objective function maximized? 3) A wine estate produces white wine and red wine. One bottle of white wine requires $20.00 of capital costs and 6 hours of labor to produce. Meanwhile, one bottle of red wine requires $25.00
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This note was uploaded on 12/07/2010 for the course MATH Math 121 taught by Professor Beaulieu during the Fall '10 term at UMass (Amherst).