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 variable ≥ 0 Which of the following points (X,Y)is not a feasible corner point?

A feasible solution to a linear programming problem

Consider the following linear programming problem: Maximize 10X + 30Y Subject to: X + 2Y ≤ 80 8X + 16Y ≤ 640 4X + 2Y ≥ 100 X, Y ≥ 0 This is a special case of a linear programming problem in which

Which of the following is not an assumption of LP?

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.Which of these is an appropriate constraint for Wicker?

A company can decide how many additional labor hours to acquire for a given week.Subcontractor workers will only work a maximum of 20 hours a week.The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C.In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C.Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C.Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C.Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr.The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost. (a)Formulate this as a linear programming problem. (b)Find the optimal solution.

When a constraint line bounding a feasible region has the same slope as an isoprofit line

Resource mix problems use LP to decide how much of each product to make, given a series of resource restrictions.

The term surplus is associated with ≥ constraints.

The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is defined as the feasible region in graphical linear programming.

One of the assumptions of LP is "proportionality."

In order for a linear programming problem to have a unique solution, the solution must exist

The solution to a linear programming problem must always lie on a 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 an appropriate objective function for this scenario?

Determine where the following two constraints intersect. 5X + 23Y ≤ 1000 10X + 26Y ≤ 1600

Management resources that need control include machinery usage, labor volume, money spent, time used, warehouse space used, and material usage.

In a minimization problem, the isocost line is used rather than an isoprofit line.

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?

The existence of non-negativity constraints in a two-variable linear program implies that we are always working in the northwest quadrant of a graph.

What is George Dantzig's contribution to linear programming?