Reference no: EM13889639
1. Discuss the role of sensitivity analysis in Linear Programming. Under what circumstances is it needed, and under what conditions do you think it is necessary?
2. A linear program has a maximum profit of $600. One constraint in this problem is 4X + 2Y <= 80. Using a computer we find the dual price for this constraint is 3, and there is a lower bound of 75 and an upper bound of 100. Explain what this means.
3. The seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned every two weeks, output is increased. The pruning process, however, requires considerably more labor than permitting olives to grow on their own and results in a smaller olive size. It also, though, permits olive trees to be spaced closer together. The yield of 1 barrel of olives by pruning requires 5 hours of labor and 1 acre of land. the production of a barrel of olives by the normal process requires only 2 labor hours but takes 2 acres of land. An olive grower has 250 hours of labor available and a total of 150 acres for growing. Because of the olive size difference, a barrel of olives produced on pruned trees sells for $20, whereas a barrel of regular olives has a market price of $30. The grower has determined that because of uncertain demand, no more than 40 barrels of pruned olives should be produced.
Use the above information to answer the following questions. You do not need to solve the problem but complete the following:
a. State, in words, the objective for the vineyard
b. Define all decision variables along with their proper units
c. Write, mathematically, the objective function
d. State, in words, the constraints faced by the vineyard
e. Write, mathematically, the constraints faced by the vineyard
4. Consider the following LP problem:
Maximize profit = 5X + 6Y
subject to 2X + Y <= 120
2X + 3Y <= 240
X,Y >= 0
- Enter into Excel and solve. Do not solve graphically.
Answer questions (a) through (c)
(a) What is the optimal solution to this problem?
(b) If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution?
(c) Instead of an increase in the profit coefficient X to $8, suppose that profit was overestimated and should only have been $3. Does this change the optimal solution?