In what follows, use the a b button and select a b for variables with subscripts. For (or ) type in = and Mbius will

In what follows, use the a^b button and select a_b for variables with subscripts. For (or ) type in <= or >= and Mbius will covert this entry to the symbol. In this questions you are asking to write things 'in order'. This refers to the usual numbering we apply to variables in primal and dual programs.

Consider the primal linear program

Max z=7x1+3x2z=7x1+3x2

subject to

10x1+x24

4x1+2x25,

x1,x20

Write down the dual program. Enter the dual objective function: a) w=

b) If the structural constraints are ordered in the usual way, enter the first constraint:

c) Enter the second constraint:

d) You do not have to enter the non-negativity constraints, but remember that they are still part of the dual program. Solve the dual program using the dual simplex method. Enter a matrix with two rows and four columns containing the entries of the final simplex tableau beneath the objective row.

e) Enter the optimal coordinates of an optimal point. y1=

f) y2=

g) optimal value of w

h) Write down the complementary slackness equations, substitute in your values for y1 and y2, and solve to get the optimal value of x1 and x2 for the primal program. Enter these values: x1=

i) x2=