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1 answer:
Answer: The maximum value: P = 6x + 7y - 2 is 84 at (5,8).
Step-by-step explanation:
Here, Object of constraint P(max) = 6x + 7y - 2.
And, the system of constraints,
x≤5, y≤(1/5)x + 7, x≥0, y≥0
Since, x= 5 is a line parallel to y-axis.
And at origin it is giving 0≤5 ( false)
Thus the area of inequality x≤5 does not contain the origin.
Now, x -intercept and y-intercept of line y=(1/5)x + 7 are (-35,0) and (0, 7) respectively.
Also, at (0, 0), 0 ≤(1/5)×0 + 7 (true)
Therefore, inequality y≤(1/5)x + 7 will contain the origin.
Now, x≥0, y≥0 shows the first quadrant.
Thus, we get feasible region ABCD.
In which at A≡(0,7), P = 49.
At B≡(5,8), P= 84,
At C≡(5,0), P= 30,
And, D≡(0,0), P= 0
Therefore at B, P is maximum.
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<h2>Hello!</h2>
The answer is:
Center: (1,-2)
Radius: 4 units.
<h2>Why?</h2>To solve the problem, using the given formula of a circle, we need to find its standard equation form which is equal to:
Where,
"h" and "k"are the coordinates of the center of the circle and "r" is its radius.
So, we need to complete the square for both variable "x" and "y".
The given equation is:
So, solving we have:
Now, we have that:
So,
Center: (1,-2)
Radius: 4 units.
Have a nice day!
Note: I have attached a picture for better understanding.