PROBLEMThe seasonal yield of olives in a Piraeus, Greece, vineyard is greatly influenced by a process of branch pruning. If olive trees are pruned eve
ry 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 solutionb) Optimum valuec) Slack variabled) Range of Optimalitye) Range of Feasibilityf) Shadow Priceg) Binding Constraintsh) Non-binding constraintsi) Feasible Region5) 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 applicableb) Give one example where the optimal solution is not applicable9) In graphical method analysis, when it comes to simultaneous changes for RHS of constraints:a) Give one example where the shadow price is applicableb) Give one example where the shadow price is not applicable10) Interpret all your finding correspond to the problem given.