Question

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.

Answer 1

Answer:

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