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 [tex]2x+y\geq 8[/tex] -------(1)
[tex]x+y \geq 6[/tex] ------------- (2)
[tex]x \geq 0[/tex], [tex]y \geq 0[/tex] -------- (3)
Since, For equation 1) x-intercept, (4, 0) and y-intercept (0,8)
And, [tex]2\times 0+0\geq 8[/tex]⇒[tex]0\geq 8[/tex] ( 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, [tex] 0+0\geq 6[/tex]⇒[tex]0\geq 6[/tex] ( 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
