Exam 7: Linear Programming Models: Graphical and Computer Methods

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 in the feasible region?

A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called

Which of the following constraints are binding?

How does the case of alternate optimal solutions, as a special case in linear programming, compare to the two other special cases of infeasibility and unboundedness?

Consider the sensitivity report above. (a)If the current solution shows a maximum profit of $200, what is the profit if Chow Chow is increased from $2.25 to $2.50? (b)If the current solution shows a maximum profit of $200, what is the profit if Tomato is decreased from $1.95 to $1.75?

Susanna Nanna is the production manager for a furniture manufacturing company.The company produces tables (X)and chairs (Y).Each table generates a profit of $80 and requires 3 hours of assembly time and 4 hours of finishing time.Each chair generates $50 of profit and requires 3 hours of assembly time and 2 hours of finishing time.There are 360 hours of assembly time and 240 hours of finishing time available each month.The following linear programming problem represents this situation. Maximize 80X + 50Y Subject to: 3X + 3Y ≤ 360 4X + 2Y ≤ 240 X, Y ≥ 0 The optimal solution is X = 0, and Y = 120. (a)What would the maximum possible profit be? (b)How many hours of assembly time would be used to maximize profit? (c)If a new constraint, 2X + 2Y ≤ 400, were added, what would happen to the maximum possible profit?

One of the assumptions of LP is "simultaneity."

The Greatest Generation Food Company wishes to introduce a new brand of pureed ready-to-eat meals (composed of pureed chicken and pureed liver meat products)that meets certain nutritional requirements.The liver-flavored product contains 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored product contains 1 unit of nutrient A and 4 units of nutrient B.According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new meals.In addition, the company has decided that there can be no more than 15 units of liver-flavored meat product in a package.It costs 1 cent to make a liver-flavored product and 2 cents to make a chicken-flavored product.At what point does the optimal solution exist?

The optimal solution to this linear program is

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.What should the objective function be?

List the 7 properties of linear programs.

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 objective function?

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

In the term linear programming, the word programming comes from the phrase "computer programming."

Billy Penny is trying to determine how many units of two types of lawn mowers to produce each day.One of these is the Standard model, while the other is the Deluxe model.The profit per unit on the Standard model is $60, while the profit per unit on the Deluxe model is $40.The Standard model requires 20 minutes of assembly time, while the Deluxe model requires 35 minutes of assembly time.The Standard model requires 10 minutes of inspection time, while the Deluxe model requires 15 minutes of inspection time.The company must fill an order for 6 Deluxe models.There are 450 minutes of assembly time and 180 minutes of inspection time available each day.How many units of each product should be manufactured to maximize profits? Let X = number of Standard models to produce Y = number of Deluxe models to produce Maximize 60X + 40Y Subject to: 20X + 35Y ≤ 450 10X + 15Y ≤ 180 Y ≥ 6 X, Y ≥ 0

Consider the following linear programming problem: Maximize 20X + 30Y Subject to: X + Y ≤ 80 12X + 12Y ≤ 600 3X + 2Y ≤ 400 X, Y ≥ 0 This is a special case of a linear programming problem in which

Unlike a maximization problem, a two-variable minimization problem may not be solved graphically.

Which of the following is not one of the steps in formulating a linear program?

You can actually take in $453.60 with this setup.If you had only one more cup of granulated sugar what could your profit be?

Define alternate optimal solutions with respect to an LP solution.