Answer: C minimum is 42 for (6,0).
Step-by-step explanation: We are given cost function C= 7x+8y.
Also we are given constraints on x and y.
2x+y > 8
x+y>6
x>0
y>0
We need to find the minimum value of the given function.
In order to find the minimum value for the given function and for the given constraints, we need to graph the given inequalities first.
And plot the vertices of the feasible region.
For the feasible region we got coordinates of the vertices (0,8), (2,4) and (6,0).
Now, plugging those coordinates in given function C= 7x+8y one by one.
For (0,8) coordinate, we get
C = 7(0) +8(8) = 0 + 64 = 64.
For (2,4)
C = 7(2) +8(4) = 28 + 32 = 60.
For (6,0)
C = 7(6) +8(0) = 42+0 = 42.
We got lowest value 42.
Therefore, the minimum value of C= 7x+8y is 42.