Find the maximum possible value and the minimum possible value of the objective function f= 4x + 2y subject to the following constraints. 3x + y ≤ 12 x + 2y ≤9 -x+y≤3 x20, y 20 The maximum value of the objective function subject to the constraints is The minimum value of the objective function subject to the constraints is 8 6 4 (0.3) 2 (0,0) 2 (14) 3x+y=12 (3,3) -x+y=3 *+2y=9 (4,0) 6 >X

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.  Suppose a sample of 2552 tenth graders is drawn. Of the students sampled, 2119 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Find the absolute maximum and minimum values of the function, subject to the given constraints. 2 2 k(x,y)= -x -y +6x+6y; 0≤x≤ 4, y ≥0, and x+y≤8 The minimum value of k is 1. (Simplify your answer.) The maximum value of k is (Simplify your answer.)

Find the maximum value of the objective function z = 8x + 2y, subject to the following constraints. (See Example 2.) 5x + y ≤ 35 3x + y ≤ 27 x ≥ 0, y ≥ 0 The maximum value is z = at (x, y) = Additional Materials BeBook