The graph to the right shows a region of feasible solutions. Use this region to

Question

The graph to the right shows a region of feasible solutions. Use this region to find maximum and minimum values of the given objective functions, and the locations10- of these values on the graph. (2, 8) (a) z 2x+3y (b) z = x + 4y (a) What is the maximum of z 2x + 3y? Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. (7, 3) O A. and is The maximum value of the objective function z-2x + 3y is located at the point (Type an exact answer.) 0- 10 B. The maximum does not exist.

Explanation / Answer

The feasible region lies within (2, 8), (0, -5), (7, 3) and (3, 1). So finding the maximum and minimum objective value is quite simple task. Just place the co-ordinates in the equation and see which set gives you the maximum value -

1. Using (2, 8) -

z = 2(2) + 3(8)

=> z = 28

2. Using (7, 3) -

z = 2(7) + 3(3)

=> z = 23

3. Using (3, 1) -

z = 2(3) + 3(1)

=> z = 9

4. Using (0, -5) -

z = 2(0) + 3 (-5)

=> z = -15

The maximum and minimum objective values of the function z = 2x + 3y are:

Maximum: 28 at (2,8)

Minimum: -15 at (0 -5)

1. Using (2, 8) -

z = (2) + 4(8)

=> z = 34

2. Using (7, 3) -

z = (7) + 4(3)

=> z = 19

3. Using (3, 1) -

z = (3) + 4(1)

=> z = 7

4. Using (0, -5) -

z = (0) + 4(-5)

=> z = -20

Maximum and Minimum objective values of z = x + 4y are:

Maximum: 34 at (2, 8)

Minimum: -20 at (0, -5)

Answering the (a) part asked in question -

The maximum value of the objective function z = 2x + 3y is 28 and is located at the point (2, 8).

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