Question $5$

d$.$ Consider the following linear programming problem:

Min $A+2B$

s$.$t$.$

$A+4B21$

$2A+B7$

$3A+1\mathrm{.}5B21$

$-2A+6B0$

$A,B0$

a$.$ Find the optimal solution using the graphical solution procedure and the value of the objective function.

b$.$ Determine the amount of slack or surplus for each constraint.

c$.$ Suppose the objective function is changed to max $5A+2B.$ Find the optimal solution and the value of the objective function.

Question $6$

Does the following linear program involve infeasibility, unbounded, and$/$or alternative optimal solutions? Explain.

Max $4A+8B$

s$.$t$.$

$2A+2B10$

$-1A+1B8$

$A,B0$