Answer to Question #193409 in Operations Research for muuz

Question

assume you are given the following linear programming model. max z= 2x1 + 3x2, subject to x1+x2<20, 2x1+4x2<60, x1>0, x2>0. compute a unit profit allowable range(range of optimal) for chair and table interpret your answer

Answer 1

Given:

Max z=2x₁+3x₂

Subject to the constraints,

x₁+x₂<20

2x₁+4x₂<60

x₁,x₂>0

Calculation:

Use an online graphing calculator and obtain the bounded region of the given constraint as shown below.

From the above Figure the corner points are observed to be (0,0), (0,15),(10,10) and (20,0)

Compute the optimal solution as follows.

The max value of z is obtained at (10,10)

Max z=50.

Hence a unit profit allowable range(range of optimal) for chair and

table is 50

An interpretation of this is that the unit contains all lower values for the coefficient and ... of the objective function without causing the optimal basis to change.