Question

Find the minimum and maximum values of z = 3x + 4y, if possible, for the following set of constraints. 5x + 8y 240 X+ 8y 2 16 x20, 720 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. Click to select and enter your answer(s) and Check Answer. 1 part remaining Clear All

Answer 1

The equations, 5x+8y= 40 and x+8y=16 are plotted in an xy graph using the following the following tables.

For 5x+8y= 40,

Value of x	Value of y	Value of equation
0	y	5
x	0	8

For x+8y=16

After plotting the xy graph, the feasible region will be obtained with the following coordinates. A (0,0) , B (0,2), C (8,0) and D( a,b). To find the coordinates of D, we have to solve the equations

5x + 8y =40 -(1)

x + 8y = 16 -(2)

Subtracting (1) by (2) gives,

4x = 24

x = 6

Substituting the value of x in (2) gives,

6 + 8y = 16

8y = 10

y= (5/4)

Hence the coordinates of D is (6,5/4).

Therefore,

Coordinates	Value of z = 3x + 4y
A (0,0)	3(0) + 4(0) =0
B (0,2)	3(0) +4(2) = 8
C (8,0)	3(8) + 4(0) = 24
D (6,5/4)	3(6) + 4(5/4) = 23

As per the above table, the minimum value is 0 which occurs at origin (0,0) and maximum value is 24 which occurs at (8,0).