Answer:
9
Explanation:
You want the minimum value of objective function C=6x+3y, given the constraints x>1, y≥1, 4x+2y<32, and 2x+8y<56.
Minimum
The objective function has positive coefficients for both x and y, so it will be minimized when x and y are at their minimum values. The constraints tell you these minimum values are x=1 and y=1, so the minimum value of C is ...
C = 6(1) +3(1) = 9
The minimum value of C is 9.
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Additional comment
The value of x cannot actually be 1, so the value of C cannot actually be 9. However x may be arbitrarily close to 1, so C may be arbitrarily close to 9.
C = 6x +3y ⇒ x = (C -3y)/6
The x-constraint requires ...
x > 1
(C -3y)/6 > 1
C -3y > 6 . . . . . . multiply by 6
C > 6 +3y . . . . . . add 3y
The minimum value of y is exactly 1, so we have ...
C > 6 +3(1)
C > 9