Question

Find the maximum value of the function z = 2x+8y. subject to the following constraints.

a)x>2
b)y>3
c)4x + 7y =57
d)Z=0
e)Х

Answer 1

To find the maximum value of z = 2x + 8y given the constraints, graph the constraints to form a feasible region, identify corner points, evaluate the function at these points, and determine the highest value of z.

Step-by-step explanation:

The question is about finding the maximum value of the linear function z = 2x + 8y, given certain constraints. To solve this, we can use linear programming techniques or graphical methods. Since the constraints include inequalities and a linear equation, we can graph these constraints to form a feasible region and then evaluate the function at the corner points of this region to find the maximum value.

Steps to find the maximum value:

1. Graph the constraints to determine the feasible region.
2. Identify the corner points of the feasible region.
3. Evaluate the function z = 2x + 8y at each corner point.
4. Determine which point gives the highest value of z, which will be the maximum value.

In this case, the equation 4x + 7y = 57 is one constraint that forms a line, and the inequalities x > 2 and y > 3 restrict the feasible area to above and to the right of these values, respectively. The maximum value of z is found by evaluating the objective function at these intersection points and comparing the results.