Exam 7: Linear Programming Models: Graphical and Computer Methods

Suppose a linear programming (minimization)problem has been solved and the optimal value of the objective function is $300.Suppose an additional constraint is added to this problem.Explain how this might affect each of the following: (a)the feasible region. (b)the optimal value of the objective function.

As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special.The profit on the Deluxe model is $12 per unit, and the Special's profit is $10.Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage.Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time.Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.The company has also decided that the Special model must comprise at most 60 percent of the production total. Formulate this as a linear programming problem.

The shadow price is the same as the dual price in maximization problems.

If you enter inequalities such as "≤" directly into your Excel spreadsheet, you do not need to designate them when defining constraints using Solver.

The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred to as

Consider the following linear programming problem: Maximize 5X + 6Y Subject to: 4X + 2Y ≤ 420 1X + 2Y ≤ 120 All variables ≥ 0 Which of the following points (X,Y)is feasible?

When using Solver to find a solution for an LP problem, both the left-hand side and the right-hand side of your constraints must be a formula calculated using the cells containing the decision variables.

The corner point solution method

Consider a product mix problem, where the decision involves determining the optimal production levels for products X and Y.A unit of X requires 4 hours of labor in department 1 and 6 hours of labor in department 2.A unit of Y requires 3 hours of labor in department 1 and 8 hours of labor in department 2.Currently, 1000 hours of labor time are available in department 1, and 1200 hours of labor time are available in department 2.Furthermore, 400 additional hours of cross-trained workers are available to assign to either department (or split between both).Each unit of X sold returns a $50 profit, while each unit of Y sold returns a $60 profit.All units produced can be sold.Formulate this problem as a linear program.(Hint: Consider introducing other decision variables in addition to the production amounts for X and Y.)

What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?

Two advertising media are being considered for promotion of a product.Radio ads cost $400 each, while newspaper ads cost $600 each.The total budget is $7,200 per week.The total number of ads should be at least 15, with at least 2 of each type.Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people.The company wishes to reach as many people as possible while meeting all the constraints stated.How many ads of each type should be placed?

In a minimization problem, the isocost line slides down and to the left through a feasible region to reflect decreasing costs.

Define unboundedness with respect to an LP solution.

Classic New Orleans desserts include pralines and Bananas Foster - both are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen.Your first constraint for a graphical solution has been plotted.Which constraint is it?

Which of the following is not a part of every linear programming problem formulation?

Consider the sensitivity report below: (a)Which constraints are binding? (b)Which constraints are non-binding? (c)What is the increase in the objective value if 3 Coffee are added?

Classic New Orleans desserts include pralines, pecan pie and Bananas Foster - all three are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A pecan pie takes two cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon of vanilla, and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen and a pecan pie costs $22.40.Which of these is an appropriate constraint?

Two models of a product - Regular (X)and Deluxe (Y)- are produced by a company.A linear programming model is used to determine the production schedule.The formulation is as follows: Maximize profit = 50X + 60Y Subject to: 8X + 10Y ≤ 800 (labor hours) X + Y ≤ 120 (total units demanded) 4X + 5Y ≤ 500 (raw materials) All variable ≥ 0 The optimal solution is X = 100, Y = 0. How many units of the regular model would be produced based on this solution?

Which of the following is not an assumption of LP?

Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility of multiple solutions.