Question

Please help!! (Picture is shown above)

Answer 1

Answer:

(³/₂, 5)  

Step-by-step explanation:

The limitation that x ≥ 0 and y ≥0 limits us to the first quadrant.

1. Plot the two inequalities

See the diagram below.

The graph of y ≤ ⅔x + 4 is represented by the red line and the red area below it.

The graph of 8 ≥ y + 2x is represented by the blue line and the blue area below it.

The purple area is the region in which all conditions are satisfied.

2. Determine the point at which the two lines intersect

$\begin{array}{rcl}y & = & \dfrac{2}{3}x + 4\\8 & = &y + 2x\\\\3y & = & 2x+12\\y & = & -2x + 8\\\\4y & = & 20\\\mathbf{y} & = & \mathbf{5}\\8 & = & 5 + 2x\\2x & = & 3\\\mathbf{x} & = &\mathbf{\dfrac{3}{2}}\\\\\end{array}\\\text{The two graphs intersect at \textbf{(1.5, 5)} }$

3. Determine the equation for D

The line should include the point (1.5, 5)

D = 6x -3y = 6×1.5 - 3×5 = 9 - 15 = -6

The equation of the objective function is

6x - 3y = -6  

It is represented by the black line in the diagram and its maximum occurs at

(³/₂, 5)

Answer 2

You can type those equations into the desmos graphing calculator online! find the feasible region (where all the colors overlap) and find the vertices then fill them into the objective function! if you have any more questions then let me know!!