Graphically solve the following problem.You need not show the graph.However, you would need to draw one to solve the problem correctly.For Part (a), solvethe problem mathematically to identify the intersection points.

Maximizeprofit = 8x1 + 5x2

Subject to:

X1 + 2X2 <=16

2X1+X2<= 20

x1, x2 >= 0

(a).What is the optimal solution based on the graph? Identify all the corner points and the corresponding profit values.Compare that with the solution you get using the software.

(Use QM for Windows or ExcelQM to answerbtoe).

(b).Change the right-hand side of constraint 1 to 17 (instead of 16) and resolve the problem.How much did the profit increase or decrease by as a result of this?What is the new solution?

(c).Change the right-hand side of constraint 1 to 13 (instead of 16) and resolve the problem.How much did the profit decrease or increase by as a result?What would happen ifthe right-hand-side value were to go below 10?

(d).Change the right-hand side of constraint 2 to 22 (instead of 20) and resolve the problem.How much did the profit decrease from the original amount as a result of this?Identify the new solution.

(e).What happens to the optimal solution if profits from X1 are reduced to $6?

(f).Examine the following output from QM.What is the dual price of constraint 1?What is the lower bound on this?

Linear Programming ResultsPart (f)X1X2RHSDualMaximize85Const 1

12<=160.67Const 221<=203.67Solution8484

Ranging

VariableValueReducedOriginal ValueLower BoundUpper BoundX18082.510X2405416

Constraint

Dual ValueSlack/SurplusOriginal ValueLower BoundUpper BoundConstraint 10.670161040Constraint 23.67020832

(g).What conclusions can you draw from the results of this table regarding bounds of the right-hand-side values and the dual price?