Exam 7: Linear Programming Models: Graphical and Computer Methods

A constraint with zero slack or surplus is called a

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?

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.What is the minimum cost?

Consider the following linear programming problem: Minimize 20X + 30Y Subject to: 2X + 4Y ≤ 800 6X + 3Y ≥ 300 X, Y ≥ 0 What is the optimum solution to this problem (X,Y)?

A straight line representing all non-negative combinations of X₁ and X₂ for a particular profit level is called a(n)

Upon retirement, Mr.Klaws started to make two types of children's wooden toys in his shop-Wuns and Toos.Wuns yield a variable profit of $9 each and Toos have a contribution margin of $8 each.Even though his electric saw overheats, he can make 7 Wuns or 14 Toos each day.Since he doesn't have equipment for drying the lacquer finish he puts on the toys, the drying operation limits him to 16 Wuns or 8 Toos per day. (a)Solve this problem using the corner point method. (b)For what profit ratios would the optimum solution remain the optimum solution?

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. (a)Formulate this as a linear programming problem. (b)Find the solution that gives the maximum profit.

Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y ≤ 480 2X + 3Y ≤ 360 All variable ≥ 0 The maximum possible value for the objective function is

An objective function is necessary in a maximization problem but is not required in a minimization problem.

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

A plastic parts supplier produces two types of plastic parts used for electronics.Type 1 requires 30 minutes of labor and 45 minutes of machine time.Type 2 requires 60 minutes of machine hours and 75 minutes of labor.There are 600 hours available per week of labor and 800 machine hours available.The demand for custom molds and plastic parts are identical.Type 1 has a profit margin of $25 a unit and Type 2 has a profit margin of $45 a unit.The plastic parts supplier must choose the quantity of Product A and Product B to produce which maximizes profit. (a)Formulate this as a linear programming problem. (b)Find the solution that gives the maximum profit using either QM for Windows or Excel.

Any linear programming problem can be solved using the graphical solution procedure.

The addition of a redundant constraint lowers the isoprofit line.

What is the most you would pay for one more cup of brown sugar?

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, and there should be no more than 19 ads in total.The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent.Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond.The company wishes to reach as many respondents as possible while meeting all the constraints stated.Develop the appropriate LP model for determining the number of ads of each type that should be placed.

Consider the following linear programming problem: Maximize 5X + 6Y Subject to: 4X + 2Y ≤ 420 1X + 2Y ≤ 120 All variable ≥ 0 Which of the following points (X,Y)is not feasible?

Define infeasibility with respect to an LP solution.

Solve the following linear programming problem using the corner point method: Maximize 3X + 5Y Subject to: 4X + 4Y ≤ 48 1X + 2Y ≤ 20 Y ≥ 2 X, Y ≥ 0

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 constraint for the finishing time?

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. Which of these constraints is redundant?