Question

For each of the following two LP models, respond to the following questions using graphic tools and algebraic methods only:

1. Identify the constraints that are binding and the ones that are not binding.
2. Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility region)
3. Find the range of optimality of both of the objective function coefficients
4. Find the shadow prices of each of the constraints
5. Compute the amount by which the objective function changes, if the right-hand side of one of the constraints increases by 8%.

Model 1:
Maximize f = 4x + 7y subject to the following constraints:

x	+	2y	≤	7
5x	+	3y	≤	12
		y	≤	3

x and y are non-negative
 
 Model 2
Maximize f = 7x + 5y subject to the following constraints:

3 x	+ 4	y	≤	24
2x	+	1y	≤	10
		x	≥ 1

          y  ≤  5
x and y are non-negative