The vertices are not given in the order.

A = (0, 0); B (12, 0) ; C(12, 5) ; D(0, 5)

We need to evaluate the value of Q at the vertices , on the boundaries of lines AB, BC, CD, DA and inside the rectangle given by the constraint equations.

The equations corresponding to the sides of the rectangle ABCD:

AB : (y - 0)/(x-0) = 0/12 => y = 0

BC : x = 12

CD : y = 5

DA: x = 0

The region inside and on the sides of the rectangle is given by the constraints:

0 ≤ x ≤ 12 and 0 ≤ y ≤ 5

a)

Q = 7 x + 14 y

as the values of x and y are non-negative, it is easy to see the maximum and minimum values of Q.

Minimum value of Q at A ( 0, 0) : 0

Maximum value of Q at C (12, 5) : 7 *12 + 14 * 5 = 154

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b) we know x and y are non-negative.

Q = - 9 x + 20 y

It is easy to see that Q is maximum when y is maximum and x is minimum.

Max value of Q at D(0, 5) : - 9 * 0 + 20 * 5 = 100

Also, Q is minimum when x is maximum and y is minimum.

MAx value of Q at B (12, 0): -9 * 12 + 20 * 0 = -108.