Question

Draw the feasible set for the following system of linear inequalities.L1:x>=0L2:y>=0L3: -x+y<=1L4: x+y<=2Maximize the objective function f= x+2y subject to the constraints in A. You should find the values x and y that yield the maximum and also compute the maximum How would you be able to set up the linear programming problem?

Answer 1

The system of inequalities can be plotted using a graphing calculator. The graph of the system of inequalities is shown below:

The solution to the system of equations is given to be the unshaded region.

The objective function is given to be:

$f=x+2y$

The constraints of the graph of the system of inequalities are shown in the diagram below:

The constraints are:

$(x,y)=(0,0),(0,1),(2,0),(0.5,1.5)$

The values of f at the constraints are calculated as follows:

At (0, 0)

$\begin{gathered} f=0+2(0) \\ f=0 \end{gathered}$

At (0, 1)

$\begin{gathered} f=0+2(1) \\ f=2 \end{gathered}$

At (2, 0)

$\begin{gathered} f=2+2(0) \\ f=2 \end{gathered}$

At (0.5, 1.5)

$\begin{gathered} f=0.5+2(1.5)=0.5+3 \\ f=3.5 \end{gathered}$

Therefore, the maximum can be gotten at (0.5, 1.5).