Question 1 Form the dual maximization problem (Use x 1 , x 2 , and x 3 as the variables and f as the function ) and use the simplex method to solve the minimization problem Assume that all variables are nonnegative Minimize g 14 y 1 13 y 2 , subject to the following y 1 y 2 100 2 y 1 y 2 140 6 y 1 5 y 2 580 Maximize f subject to 14 13 x 1 , x 2 , x 3 0 The minimum value of the objective function is which occurs at ( y 1 , y 2 ) Question 2 A function and the graph of a feasible region are given f 4 x 5 y The x y coordinate plane is given Two lines and a shaded region are on the graph The line x 2 y 19enters the window on the positive y axisbelow the other line, goes down and right, crosses the line3 x 2 y 29,and ends on the positive x axis The line3 x 2 y 29enters the window on the positive y axisabove the other line, goes down and right, crosses the line x 2 y 19,and exits the window on the positive x axis The shaded region is above the two lines, right of the y axis,and above the x axis Find both the maximum and minimum values of the function, if they exist, and the point at which each occurs (If an answer does not exist, enter DNE )The maximum value of the objective function is which occurs at ( x , y ) The minimum value of the objective function is which occurs at ( x , y )

Question

Question  1 Form the dual maximization problem (Use x 1 , x 2 , and x 3 as the variables and f as the function ) and use the simplex method to solve the minimization problem  Assume that all variables are nonnegative Minimize g  14 y 1  13 y 2 , subject to the following  y 1   y 2 100 2 y 1   y 2 140 6 y 1   5 y 2 580 Maximize f   subject to                             14                           13 x 1 , x 2 , x 3 0   The minimum value of the objective function is                which occurs at ( y 1 , y 2 )                Question  2 A function and the graph of a feasible region are given  f  4 x  5 y The x y coordinate plane is given  Two lines and a shaded region are on the graph  The line x   2 y   19enters the window on the positive y  axisbelow the other line, goes down and right, crosses the line3 x   2 y   29,and ends on the positive x  axis  The line3 x   2 y   29enters the window on the positive y  axisabove the other line, goes down and right, crosses the line x   2 y   19,and exits the window on the positive x  axis  The shaded region is above the two lines, right of the y  axis,and above the x  axis  Find both the maximum and minimum values of the function, if they exist, and the point at which each occurs  (If an answer does not exist, enter DNE )The maximum value of the objective function is                which occurs at ( x , y )             The minimum value of the objective function is          which occurs at ( x , y )

Accepted Answer

The Answer is in the image, click to view ...

y₁	+	y₂	100
2y₁	+	y₂	140
6y₁	+	5y₂	580

Question

Question #1 Form the dual maximization problem (Use x 1 , x 2 , and x 3 as the variables and f as the function.)

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