Which ordered pair maximizes the objective function P = 3x + 8y?
(0, 0); (2, 7); (5, 6); (8, 1)

Solution:

A linear function of the form Z = ax + by, where a and b are constant, which has to be minimized or maximized is called a linear objective function.

Consider an example, Z = 15x + 15y. This is a linear objective function. The variables x and y are called decision variables.

It is given that

P = 3x + 8y

Substitute each ordered pair to determine the one which maximizes the function

P = 3 (0) + 8 (0) = 0

P = 3 (2) + 8 (7) = 6 + 56 = 62

P = 3 (5) + 8 (6) = 15 + 48 = 63

P = 3 (8) + 8 (1) = 24 + 8 = 32

Therefore, (5, 6) maximizes the objective function.

Which ordered pair maximizes the objective function P = 3x + 8y?
(0, 0); (2, 7); (5, 6); (8, 1)

Summary:

The ordered pair which maximizes the ordered function P = 3x + 8y is (5, 6).