Answer: The minimum value of C is 46.
Step-by-step explanation:
Since, Here, We have to find out Min C = 7x+8y
Given the constraints are \(2x+y\geq 8\) -------(1)
\(x+y \geq 6\) ------------- (2)
\(x \geq 0\), \(y \geq 0\) -------- (3)
Since, For equation 1) x-intercept, (4, 0) and y-intercept (0,8)
And, \(2\times 0+0\geq 8\)⇒\(0\geq 8\) ( false)
Therefore the area of line 1) does not contain the origin.
For equation 2) x-intercept, (6, 0) and y-intercept (0,6)
And, \(0+0\geq 6\)⇒\(0\geq 6\) ( false)
Therefore the area of line 2) does not contain the origin.
Thus after plotting the constraints 1) 2) and 3) we get Open Shaded feasible region AEB ( Shown in below graph)
At A≡(0,8) , C= 64
At E≡(2,4), C= 46
At B≡(6,0), C= 42
Thus at B, C is minimum, And its minimum value = 42
