Consider the following mixed-integer linear program:

Max	3x1 + 4x2
s.t.
	5x1 + 8x2 40
	7x1 + 5x2 35
	x1, x2 0 and x1 integer

1. Choose the correct graph which shows the constraints for this problem and uses boldface vertical lines to indicate all feasible mixed-integer solutions.

   (i)		(ii)
   (iii)		(iv)

   (see below for attached image)

1. Graph (i) (correct answer)
2. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. The optimal solution is given by x₁ = fill in the blank 2, x₂ = fill in the blank 3. Its value is fill in the blank 4. Round the value of x₁ down to find a feasible mixed-integer solution. If required, round your answers to two decimal places. Rounding the value of x₁ down to find a feasible mixed integer solution yields x₁ = fill in the blank 5, x₂ = fill in the blank 6 with a value of fill in the blank 7. Is this solution optimal? No Why or why not? The input in the box below will not be graded, but may be reviewed and considered by your instructor.
3. Find the optimal solution for the mixed-integer linear program. If required, round your answers to two decimal places. Solution details x₁ = fill in the blank 10, x₂ = fill in the blank 11. Its value is fill in the blank 12.

a. Choose the correct graph which shows the constraints for this problem and uses boldface vertical lines to indicate all feasible mixed-integer solutions. (i) (ii) 42 7 6 6 o 4 44 3 2+ 2 2+ 1 1+ 1 2 3 5 6 7 810 31 1 2 2 3 4 5 6 7 8 10 21 (iii) (iv) 22 8 CON 7 6 4 4 3 3 2 2 2+ 1+ 11 + 1 + 1 2 5 6 7 8 10 1 2 3 4 5 6 7 310 31 Graph (i)