Question

the objective function is z = 30x + 40y.
a. find the value of the objective function at each corner of the graphed region.
b. find the maximum value of the objective function.
c. find the minimum value of the objective function.
the value of the objective function at point b is 560.
the value of the objective function at point c is 210.
the value of the objective function at point d is

Explanation:

Step1: Identify coordinates of point D

The coordinates of point D are (0,0).

Step2: Substitute into objective function

Substitute x = 0 and y = 0 into z = 30x + 40y. So, z=30\times0 + 40\times0.

Step3: Calculate the value

z = 0.

Answer:

The value of the objective function at point D is 0.
The maximum value of the objective function:
We have values at points:

• At A(0,6): z = 30\times0+40\times6=240
• At B(4,11): z = 30\times4 + 40\times11=120 + 440=560
• At C(7,0): z = 30\times7+40\times0 = 210
• At D(0,0): z = 0

The maximum value of z is 560.

The minimum value of the objective function:
Comparing the values 240, 560, 210, 0, the minimum value of z is 0.