Question

7.2.15 Find the minimum and maximum values of z = 6x + 5y, if possible, for the following set of constraints. x + y s5 - X+ys 3 2x-ys 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The minimum value is (Round to the nearest tenth as needed.) OB. There is no minimum value. tei Rese mucce Click to select and enter your answer(s) and then click Check Answer. Succe 1 part remaining Clear All

Answer 1

Institute of 25Kulam MATHEMATICS given objective function 2 = 6x + 5y (1) and constraints are x + y ss -*+y = 3 - 9x - y = 8 Giv) we won't find max.z and miniz. we use the graphical method to find moxz ar miniz Convert given constraints to equation to find feasibi region in which objective function have their umum and minimum value tretag motto += 5 - CV -x+y = 3 - wil will Ix-xc 8

yons Vos) C1,42 (0,32 (5 ) -x-avus (-3,0) (4,0) X-UT 7co, 8) -Yaxis for intersection point e eancv) and cvij xty = 5 -x +y = 3 2y = 8 x = =y=4 61,4 = ? Similarly o(133) Intersetion point of eacvi and run = . 9x - y = 8 7+ y = 5 37 = 13 x= 13 y= 5x = si 3

Now mox 2 at o( 13 , 2 ) = Zmox = 6x13 + 5 x2 = 26 + 8 = - 26 +3.33 = 29.33 miniz there is no minimum value of 2.