1. For the linearprogram:
Max 2A +3B
s.t.
A + B ≤ 12 Constraint "1"
A + 2B ≤ 16 Constraint "2"
-3A + 2B ≤ 6 Constraint "3"
A, B≥ 0
Should be done manually (must show hand work).
a. Making "A" as the horizontal variable, graph the problem neatly. Show the feasible region. Label constraints ongraphs.
b. Solve the problem. Show work. What is the optimal "A" and "B" values? What isthe optimal objective functionvalue?
c. What are the values of slack and surplus for eachconstraint?
d. Holding the coefficient of "B" in the objective function fixed, how much can the coefficient of "A" decrease or increase so that the optimal solution does notchange?
e. Holding the coefficient of "A" in the objective function fixed, how much can the coefficient of "B" decrease or increase so that the optimal solution does notchange?
f. Suppose the coefficient of "A" changes from 2 to 3 and the coefficient of "B" changes from3to2.Willtheoptimalsolutionchange?Ifso,whatisthenewoptimalsolution?
g. Which constraints have non-zero shadow prices?Explain.
h. Find the shadow price for constraint "1" by hand (that is, show the algebra and computations).
2. For the linearprogram:
Max 3A + 4B
s.t.
2A + B ≥ 6 Constraint "1"
4A + 3B ≤ 24 Constraint "2"
B ≥ 2 Constraint "3"
2A - B ≥ 0 Constraint "4"
A, B ≥ 0
Should be done manually (must show hand work).
a. Making "A" as the horizontal variable, graph the problem neatly. Show the feasible region. Label constraints ongraphs.
b. Solve the problem. Show work. What is the optimal "A" and "B" values? What isthe optimal objective functionvalue?
3. For the linearprogram:
Min 3A +B
s.t.
4A + B ≤ 20 Constraint "1"
A + 2B ≥ 7 Constraint "2"
2.5A + 3B ≤ 30 Constraint "3"
-3A + B ≤ 0 Constraint "4"
A, B ≥ 0
Should be done manually (must show hand work).
a. Making "A" as the horizontal variable, graph the problem neatly. Show the feasible region. Label constraints ongraphs.
b. Solve the problem. Show work. What is the optimal "A" and "B" values? What isthe optimal objective functionvalue?
4. Make a neatly laid out Excel spreadsheet of the linear program of the previous problem (Problem3).
a. Submit hard copies of the following: (1) The spreadsheet itself with the optimal solutions and optimal objective value shown; (2) Excel Solver's answer report; (3)Excel Solver's sensitivityreport.
b. Withoutrerunningthelinearprogram,basedontheoutputprovidedinpart(a),what will be the objective function valueif:
(i) The right side of constraint "1" decreased by3.
(ii) The right side of constraint "2" increased by2.
(iii) The right side of constraint "3" increased by5.
(iv) The right side of constraint "4" decreased by3.
(Explain how you answered the above based only on output from part a.)