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Question 1: Minimize z=2x+y z = 2 x + y subject to 3x - y = 12 x + y = 15 x = 2, y = 3 Question 2: Maximize z=5x+y z = 5 x + y subject to x - y = 10 5 x + 3 y = 75 x = 0, y = 0 Question 3:Maximize...

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Question 1: Minimize z=2x+y z = 2 x + y subject to
3x - y = 12
x + y = 15
x = 2, y = 3
Question 2: Maximize z=5x+y z = 5 x + y subject to
x - y = 10
5 x + 3 y = 75
x = 0, y = 0
Question 3:Maximize z=4x+3y z = 4 x + 3 y subject to
2 x + 3 y = 6
4 x + y = 6
x = 0, y = 0
Question 4:
A craftswoman produces floor lamps and table lamps. Production of one floor lamp requires 75 minutes of labor, and $25 of materials. Production of one table lamp requires 50 minutes of labor, and $20 of materials. She wishes to work 40 or less hours each week, and she has at most $900 for materials per week.
If her profit is $39 per floor lamp, and $33 per table lamp, how many of each should she make each week to maximize her weekly profit?
Question 5: Find the corner points of the region:
2 x + 3 y
3x - y = -2
Question 6: Find the corner points for the region:
x + 2 y = 4
3 x - 2 y = - 12
x-y
Question 7:Find all of the region's corner points:
y > 2 x + 1
y = -x+4
Question 8: Pete's Coffee sells two blends of coffee beans, Morning Blend (MB) and South American Blend (SMB). Morning Blend is 1/3 Mexican beans and 2/3 Colombian beans, while South American Blend is 2/3 Mexican beans and 1/3 Colombian beans. The profit for Morning Blend is $3 per pound, while the profit for South American Blend is $2.50 per pound. Each day the shop can obtain up to 100 pounds of Mexican beans and up to 80 pounds of Colombian beans. How many pounds of each blend should the shop prepare each day to maximize profit?
Question 9: Find the corner points of the region:
2 x + 5 y = 70
5 x + y = 60
x = 0, y = 0
Question 10:Find the maximum and minimum of z=3x+4y z = 3 x + 4 y subject to
3 x + 2 y = 6
x + 2 y = 4
x = 0, y = 0
Answered Same Day Dec 26, 2021

Solution

Robert answered on Dec 26 2021
110 Votes
Ans. 1
The given equation for the minimization,
2 z x y 
The operational functions,
3 12
15
2, 3
x y
x y
x y
 
 
 

For the given above three equations, consider the inequality as equal sign and draw
the linear graph,
So, there are three pair of equations form and the respective vertex and objective
solution found respectively,
Vertex Lines Through Vertex Value of Objective
(6.75,8.25) 3x-y = 12; x+y = 15 21.75
(5,3) 3x-y = 12; y = 3 13 Minimum
(12,3) x+y = 15; y = 3 27

As shown in the above result for the vertex, (5,3) the value of the objective function is
13which is minimum.
The plot is as,

Ans.2
The objective function and constraints,
Max 5z x y 
The constraints are:
10
5 3 75
0, 0
x y
x y
x y
 
 
 

Vertex Lines Through Vertex Value of Objective
(13.125,3.125) x-y = 10; 5x+3y = 75 68.75 Maximum
(10,0) x-y = 10; y = 0 50
(0,25) 5x+3y = 75; x = 0 25
(0,0) x = 0; y = 0 0

Hence, for the vertex (13.125,3.125) has maximum of 68.75 .
The plot will be as,

Ans. 3
The objective function:
Max 4 3z x y 
The Constraints:
2 3 6
4 6
0, 0
x y
x y
x y
 
 
 

Solve for the vertices and calculating the x and y,
Vertex Lines...
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