What point in the feasible region maximizes the objective function constraints: x> =0 y> =0 -x+3> =y y< =1/3 x+1 objective function: c=5x-4y

1. Draw all graphs and determine the shaded region:

a) for you should take 1 and 4 quadrants (including y-axis);

b) for you should take 1 and 2 quadrants (including x-axis);

c) for you should draw the graph of the line y=-x+3 and take the bottom half-plane;

d) for you should draw the graph of the line y=1/3x+1 and take the bottom half-plane.

Then the intersection of all shaded parts is needed shaded region, quadrilateral OABC (see diagram for details).

2. Th graphs of the lines C=5x-4y will intersect this shaded region at different points. The maximum of the function could be only at vertices.

3. Find the coordinates of all vertices:

a) O(0,0) - the origin;

b) A(0,1) - the y-intercept of line y=-x+3;

c) C(3,0) - the x-intercept of line y=1/3x+1;

d) B: solve the system y=1/3x+1, y=-x+3.

-x+3=1/3x+1,

-x-1/3x=1-3,

-4/3x=-2,

x=3/2,

y=-3/2+3=3/2,

then B(3/2,3/2).

4) F(x)=5x-4y and

F(O)=0,

F(A)=5·0-4·1=-4,

F(C)=5·3-4·0=15,

F(B)=5·3/2-4·3/2=7.5-6=1.5

The maximal value of F is at point C.

Maximum value is 15 at point (3,0)

-4

step-by-step explanation:

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕