(3) Consider the following linear programming problem:
Maximize M=10x + 6y subject to the constraints
X+y > or = 6
X>or=0,y>or=0.
(a) sketch the feasible set
b) determine three point in the feasible set and calculate M at each of them
c) show that the objective functions attain no maximum value for point in the feasible set.
(4) for the furniture manufacturing problem , the constraint for the for finishing is now x + y < or = 18. The number 18 came from the fact that 18 hours are available for finishing each day. Suppose you will increase the number of hours available for finishing by one hour. The shadow price for the finishing constraint is the maximum price you would be willing to pay for that additional hour.
A) what is the new inequality for the finishing constraint? What is the corresponding linear equation?
(B) determined the optimal solution for the revised linear programming problem. What is the new maximum profit? How much was the profit increased due to the additional hour for finishing?
C) what is the shadow price for the finishing constraint
D) return to the original furniture manufacturing problem and assume that one additional hour is available for carpentry. Solve the altered problem.. And determine the shadow price for the carpentry constraint.
E) use your knowledge of the solution of the original furniture manufacturing problem and the definition of shadow price to explain why the shadow price for the upholstery constraint is 0.
Aristotle Science Academy
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