PROBLEM 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 the olives to grow on their own and results in a smaller

size olive. 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 I 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.

1) Determine the decision variables.

2) Determine the constraints.

3) Formulate a linear programming model.

4) Define:

a) Optimum solution

b) Optimum value

c) Slack variable

d) Range of Optimality

e) Range of Feasibility

f) Shadow Price

g) Binding Constraints

h) Non-binding constraints

i) Feasible Region

5) Transform the linear programming model in (3) to standard form.

6) Using graphical method analyse the phrases defined in (4)

7) Using QM software find the phrases defined in (4)

8) In graphical method analysis, when it comes to simultaneous changes for

coefficients of objective function:

a) Give one example where the optimal solution is applicable

b) Give one example where the optimal solution is not applicable

9) In graphical method analysis, when it comes to simultaneous changes for

RHS of constraints:

a) Give one example where the shadow price is applicable

b) Give one example where the shadow price is not applicable

10) Interpret all your finding correspond to the problem given.