<h2>
Answer with explanation:</h2>
The constraints are given by:
![x\geq 0\\\\y\geq 0\\\\y\leq \dfrac{1}{3}x+3\\\\5\geq y+x](https://tex.z-dn.net/?f=x%5Cgeq%200%5C%5C%5C%5Cy%5Cgeq%200%5C%5C%5C%5Cy%5Cleq%20%5Cdfrac%7B1%7D%7B3%7Dx%2B3%5C%5C%5C%5C5%5Cgeq%20y%2Bx)
- The first and second constraints tells that the solution must lie in the first quadrant including the origin )
( 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)
<u>Ques 1)</u>
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)
<u>Ques 2)</u>
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
C=6×0-4×3
i.e.
C= -12
C=6×1.5-4×3.5
i.e.
C= -5
The value of objective function is:
C=6×5-4×0
i.e.
C=30
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)