Exam 7: Linear Programming Models: Graphical and Computer Methods

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

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n)________ of the feasible region.

Consider the following linear program: Maximize 30X + 10Y Subject to: 3X + Y ≤ 300 X + Y ≤ 200 X ≤ 100 Y ≥ 50 X,Y ≥ 0 (a)Solve the problem graphically.Is there more than one optimal solution? Explain. (b)Are there any redundant constraints?

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?

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 least 40 percent of the production total.What is an appropriate objective function?

Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at a time.

Infeasibility in a linear programming problem occurs when

One basic assumption of linear programming is certainty.What does this imply and how reasonable is this assumption?

Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y ≤ 480 2X + 3Y ≤ 360 All variables ≥ 0 Which of the following points (X,Y)is feasible?

One basic assumption of linear programming is divisibility.Explain its need.

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 Corn are added?

The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called

If the addition of a constraint to a linear programming problem does not change the solution, the constraint is said to be

If the isoprofit line is not parallel to a constraint, then the solution must be unique.

Consider the following linear program. Maximize 30X + 10Y Subject to: 3X + Y ≤ 300 X + Y ≤ 200 X ≤ 100 Y ≥ 50 X,Y ≥ 0 Which of these is NOT a corner point of the feasible region?

There are no limitations on the number of constraints or variables that can be graphed to solve an LP problem.

Sensitivity analyses are used to examine the effects of changes in

A furniture company is producing two types of furniture.Product A requires 8 board feet of wood and 2 lbs of wicker.Product B requires 6 board feet of wood and 6 lbs of wicker.There are 2000 board feet of wood available for product and 1000 lbs of wicker.Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit.Formulate the problem as a linear program.

What is the increase in the objective value if 2 units of extrusion are added?

Which of the following is not a property of all linear programming problems?