Consider the following LP problem.

MAX:	2X1	+	4X2
Subject to:	X1	+	2X2		7
	X1	+	2X2		12
	X1	+	X2		3
		X1,	X2		0

(a)Use slack variables to rewrite this problem so that all its constraints are equal-to constraints. (Use S₁, S₂, and S₃ for the slack variables for the first, second, and third constraints respectively, where the constraints are presented in the same order as the original LP.)

MAX: ______________

Subject to:first constraint ________

second constraint ___________

third constraint _____________

X₁, X₂, S₁, S₂, S₃ 0

(b) Identify the different sets of basic variables that might be used to obtain a solution to the problem. (Enter your answer as a comma-separated list of sets.)

c) Of the possible sets of basic variables, which lead to feasible solutions and what are the values for all the variables at each of these solutions? What is the value of the objective function at each of the basic feasible solutions? (If the solution is infeasible, enter NA for the objective function value. Round your answers to two decimal places as needed.)

Solution	X1	X2	S1	S2	S3	Feasible?	Objective
1				0	0	--?-- Yes No
2			0		0	--?-- Yes No
3			0	0		--?-- Yes No
4		0			0	--?-- Yes No
5		0		0		--?-- Yes No
6		0	0			--?-- Yes No
7	0				0	--?-- Yes No
8	0			0		--?-- Yes No
9	0		0			--?-- Yes No
10	0	0				--?-- Yes No

(d) What is the optimal solution to the problem?

(X₁, X₂, S₁, S₂, S₃) =

(e) Which constraints are binding at your optimal solution from part (d)? (Select all that apply.)

first constraint-second constraintthird constraintNone of the constraints are bindi

Consider the following LP problem. MAX:2x1+4x2Subjectto:X1+2x27x1+2x212x1+x23x1,x20 (a) Use slack variables to rewrite this prob as the original LP.) MAX: Subject to: first constraint second constraint third constraint x1,x2,s1,s2,s30 (b) Identify the different sets of basic variables that might be used to obtain a solution to the problem. (Enter your answer as a comma-separated list of sets.) infeasible, enter NA for the objective function value. Round your answers to two decimal places as needed.) (d) What is the optimal solution to the problem? (x1,x2,s1,s2,s3)=( (e) Which constraints are binding at your optimal solution from part (d)? (Select all that apply.) first constraint second constraint third constraint None of the constraints are binding