The graph to the right shows a region of feasible solutions. Use this region to find maximum and minimum values of the given objectivefunctions, and the locations of these values on the graph.a. z = 3x + 5yb. z = 2x + 3yc. z = 5x + 2yd. z = x + 5ya. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The maximum value of z = 3x + 5y is at(Type integers or decimals.)OB. The maximum does not exist.Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The minimum value of z = 3x + 5y is(Type integers or decimals.)t exist.atOB. The minimum doesb. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The maximum value of the objective function z = 2x + 3y is(Type integers or decimals.)OB. The maximum does not exist.at4 The graph to the right shows a region of feasible solutions. Use this region to find maximum and minimum values of the given objectivefunctions, and the locations of these values on the graph.a. z = 3x + 5yb. z = 2x + 3yc. Z = 5x + 2yd. z=x+ 5ySelect the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. The minimum value of the objective function z = 5x + 2y is(Type integers or decimals.)OB. The minimum does not exist.d. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.at (OA. The maximum value of the objective function z = x + 5y is(Type integers or decimals.)OB. The maximum does not exist.Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. The minimum value of the objective function z = x + 5y is(Type integers or decimals.)OB. The minimum does not exist.atCDD

The given objective functions are: a. z=3x+5yb. z=2x+3yc. z=5x+2yd. z=x+5y Also, the points of the feasible region are: (0, 9), (2, 5), (6.5, 1), and (11, 0). We have to check whether the maxima or minima exists at the given points or not.a. z=3x+5y At (0, 9) we have,z=30+59=45 At (2, 5) we have,z=32+55=6+25=31 At (6.5, 1) we have,z=36.5+51=19.5+5=24.5 At (11, 0) we have,z=311+50=33 So we can say that, The minimum value of the objective function z=3x+5y is 24.5 at (6.5, 1). The maximum for any of the graph doesn't exist as it is infinite since the feasible region contains all the points that are shaded in the graph. So, for large values of x and y the value of the objective function is very large.b. z=2x+3y At (0, 9) we have,z=20+39=27 At (2, 5) we have,z=22+35=4+15=19 At (6.5, 1) we have,z=26.5+31=13+3=16 At (11, 0) we have,z=211+30=22 So we can say that, The minimum value of the objective function z=2x+3y is 16 at (6.5, 1). The maximum for any of the graph doesn't exist as it is infinite since the feasible region contains all the points that are shaded in the graph. So, for large values of x and y the value of the objective function is very large.c. z=5x+2y At (0, 9) we have,z=50+29=18 At (2, 5) we have,z=52+25=10+10=20 At (6.5, 1) we have,z=56.5+21=32.5+2=34.5 At (11, 0) we have,z=511+20=55 So we can say that, The minimum value of the objective function z=5x+2y is 18 at (0, 9). The maximum for any of the graph doesn't exist as it is infinite since the feasible region contains all the points that are shaded in the graph. So, for large values of x and y the value of the objective function is very large.d. z=x+5y At (0, 9) we have,z=0+59=45 At (2, 5) we have,z=2+55=2+25=27 At (6.5, 1) we have,z=6.5+51=11.5 At (11, 0) we have,z=11+50=11 So we can say that, The minimum value of the objective function z=x+5y is 11 at (11, 0). The maximum for any of the graph doesn't exist as it is infinite since the feasible region contains all the points that are shaded in the graph. So, for large values of x and y the value of the objective function is very large.