The graph to the right shows a region of feasible solutions. Use this region to findmaximum and minimum values of the given objective functions, and the locations ofthese values on the graph.a. z = 3x + 5yb. z= 4x+3yc. Z=2x+4yd. z=x+3ya. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The maximum value of z= 3x + 5y is(Type integers or decimals.)OB. The maximum does not exist.an example Get more help -Privacy Policy | Copyright © 20ZZ Pearson Education Inc. All Rights Reserved.XN4+8atWP9fiofiClear all112+QQCheck answerinsprt scdelete←backspace

A region is given in the graph having some points. Our aim is to find the minimum or maximum of the given objective functions, and also mention the location of the points in the graph where these objective functions are maximum or minimum. (a) The objective function is z= 3x+5y. Since there are four points (11, 0), (6.5, 1), (2, 4), and (0, 9), which are corner points, mentioned in the graph, check the values of the objective function on these points. At point (11, 0): z=311+50=33 At point (6.5, 1): z=36.5+51=24.5 At the point (2, 4): z=32+54=26 At the point (0, 9): z=30+59=45 After checking the values of z, it is concluded that the objective function is maximum at point (0, 9) and its maximum value is 45. Similarly, the function is minimum at point (6.5, 1), and its minimum value is 24.5.(b) The objective function is z= 4x+3y. Check the values of the objective function on the given four points. At point (11, 0): z=411+30=44 At point (6.5, 1): z=46.5+31=29 At the point (2, 4): z=42+34=20 At the point (0, 9): z=40+39=27 After checking the values of z, it is concluded that the objective function is maximum at point (11, 0) and its maximum value is 44. Similarly, the function is minimum at point (2, 4), and its minimum value is 20.(c) The objective function is z= 2x+4y. Check the values of the objective function on the given four points. At point (11, 0): z=211+40=22 At point (6.5, 1): z=26.5+41=17 At the point (2, 4): z=22+44=20 At the point (0, 9): z=20+49=36 After checking the values of z, it is concluded that the objective function is maximum at point (0, 9) and its maximum value is 36. Similarly, the function is minimum at point (6.5,1), and its minimum value is 17.(d) The objective function is z= x+3y. Check the values of the objective function on the given four points. At point (11, 0): z=11+30=11 At point (6.5, 1): z=6.5+31=9.5 At the point (2, 4): z=2+34=14 At the point (0, 9): z=0+39=27 After checking the values of z, it is concluded that the objective function is maximum at point (0, 9) and its maximum value is 27. Similarly, the function is minimum at point (6.5,1), and its minimum value is 9.5.