Given the objective function C=3x−2y and constraints x≥0, y≥0, 2x+y≤10, 3x+2y≤18, identify the corner point at which the maximum value of C occurs.

Given the objective function is and the contraints as follows:

       Substitute 0 for in .

      So, the intersecting point is .

       Substitute 0 for in .

      So, the intersecting point is .

       Substitute 0 for in .

      So, the intersecting point is .

       Substitute 0 for in .

      So, the intersecting point is .

        Add times to .

       Substitute in :

      So, the intersecting point is .

Corner points:

          The corner points are the boundary points of the bounded region of   the given constraints.

The bounded region of the given constraints is shown below.

Evaluate the objective function at these boundary points:

At :

At :

At:

At:

From the above calculated values, one can notice that the maximum value of is 15 and it is obtained at .

Hence, the maximum value of is 15 occurs at the corner point .

Lear more about the maximizing problems here: link

Step-by-step explanation:

Find  the maximum value of

C = 3x -2y  Objective function

subject to the following constraints.

Constraints

x ≥ 0

y ≥ 0                

2x + y ≤ 10  vertex 1 : when x=0 then y=10  (0,10)

3x + 2y ≤ 18 vertex 2 : y=0, then x=6          ( 6,0)

two equations together to determine vertex 3 :

3x+2y = 18

2x+y = 10

x=2, y= 6

The feasible region determined by the constraints is

shown. The three vertices are (0, 10),  and (6, 0), (0,9)

and (2,6)

First evaluate C = 3x -2 y at each of the vertices.

At (0, 10): C = 3(0) - 2(10) = -17

At (6, 0): C = 3(6) - 2(0) = 18

At ( 2,6) : C = 3(2) -2(6) = -6

At (0,9) : C = 3(0)-2(9)= -18

the maximum value occur on 18 when x=9 and y=0

d is correct

step-by-step explanation: