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trixxytang
09.07.2019 •
Mathematics
Given the system of constraints, name all vertices of the feasible region. then find the maximum value of the given objective function. constraints: x is greater than or equal to 0 y is greater than or equal to 0 y is less than or equal to 1/3x+3 5 is greater than or equal to y+x objective function: c=6x-4y
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Ответ:
Ответ:
The constraints are given by:
( Since, in the first quadrant both the x and y values are positive )
Also, the third inequality is a solid line ( since the inequality is not strict i.e. it is a inequality with a equality sign ) that passes through (-9,0) and (0,3) and the shaded region is towards the origin ( since the inequality passes the zero point test ).The fourth inequality is a solid line ( since the inequality is strict ) that passes through (5,0) and (0,5) and the shaded region is towards the origin ( since the inequality passes the zero point test)Ques 1)
The feasible region that is formed with the help of these inequality is:
Quadrilateral ABCD.
Also, the vertices of the feasible region are:
A(0,3)
B(1.5,3.5)
C(5,0)
D(0,0)
Ques 2)
We know that the objective function is checked at the boundary points of the feasible region i.e. vertices of the feasible region.
The objective function is:
C=6x-4y
We check at A(0,3)C=6×0-4×3
i.e.
C= -12
at B(1.5,3.5)C=6×1.5-4×3.5
i.e.
C= -5
at C(5,0)The value of objective function is:
C=6×5-4×0
i.e.
C=30
and at D(0,0)C=6×0-4×0
i.e.
C=0
The maximum value of the objective function is: 30
and it is obtained at the vertex C(5,0)
Ответ:
First, I would convert the fraction to from a mixed number by multiplying 3*8 and then adding 7. This gives us the fraction 31/8 to convert into a decimal. 31 divided by 8 equals 3.875.
Your answer is 3.875.
I hope this helps :)