Appalachian Industries is a furniture manufacturer that produces a bedroom suites (x1) and dining room sets (X2). The company has developed a linear programming model to determine the number of each to produce given resource constraints for wood (400 lb), and labor (120 hr). The linear programming model is Maximize: Z = 600 X1 + 400 x2 (Profit) Subject to: 200 x1 + 80 x2 $ 400 lbs (1) Shadow price = $0.71 40 x1 + 30 X2 S 120 hrs (2) Shadow price = $11.43 X1, X2 2 0 6 5 4 W N O 0developed a linear programming model to determine the nu each to produce given resource constraints for wood (400 lb), and labor (120 hr). The linear programming model is Maximize: Z = 600 x1 + 400 X2 (Profit) Subject to: 200 x1 + 80 X2 3 400 lbs (1) Shadow price = $0.71 40 x1 + 30 X2 s 120 hrs (2) Shadow price - $11.43 X1, X2 2 0 6 5 4 3 2 1 O 0 2 3 4 -Wood -Labor -Profit\fFor problem 9, what is the profit made with the optimal solution? (Round to the nearest dollar.)For problem 9, write constraint #2 in the standard format with slack variable(s). . 40 x1 + 30 X2 + 52 = 120 40 x1 + 30 X2 - 52 = 120 40 x1 + 30 x2 - $2 + A2 = 120 40 x1 + 30 x2 + 52 + A2 = 120For problem 9, how much slack is there in the Wood constraint, if you make 0.8 bedroom suites and 0.4 dining room sets? (Round your answer to the nearest integer.)