Exam 9: Linear Programming

What combination of x and y will provide a minimum for this problem? Minimize Z = $3x + $15y; Subject to: (1)2x + 4y > 12 (2)5x + 2y > 10

In the range of feasibility,the value of the shadow price remains constant.

For the products A,B,C,and D,which of the following could be a linear programming objective function?

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.What is the objective function?

Wood Specialties Company produces wall shelves,bookends,and shadow boxes.It is necessary to plan the production schedule for next week.The wall shelves,bookends,and shadow boxes are made of oak,of which the company has 600 board feet.A wall shelf requires 4 board feet,bookends require 2 board feet,and a shadow box requires 3 board feet.The company has a power saw for cutting the oak boards into the appropriate pieces; a wall shelf requires 30 minutes,bookends require 15 minutes,and a shadow box requires 15 minutes.The power saw is expected to be available for 36 hours next week.After cutting,the pieces of work in process are hand finished in the finishing department,which consists of 4 skilled and experienced craftsmen,each of whom can complete any of the products.A wall shelf requires 60 minutes of finishing,bookends require 30 minutes,and a shadow box requires 90 minutes.The finishing department is expected to operate for 40 hours next week.Wall shelves sell for $29.95 and have a unit variable cost of $17.95; bookends sell for $11.95 and have a unit variable cost of $4.95; a shadow box sells for $16.95 and has a unit variable cost of $8.95. (i)Is this a problem in maximization or minimization? (ii)What are the decision variables? Suggest symbols for them. (iii)What is the objective function? (iv)What are the constraints?

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.For the production combination of 0 American and 400 British,which resource is "slack" (not fully used)?

The linear optimization technique for allocating constrained resources among different products is:

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.What is the objective function?

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding,two minutes per unit for painting,and one minute per unit for packing.Product B requires two minutes per unit for molding,four minutes per unit for painting,and three minutes per unit for packing.There will be 600 minutes available for molding,600 minutes for painting,and 420 minutes for packing.Both products have profits of $1.50 per unit. (i)What combination of A and B will maximize profit? (ii)What is the maximum possible profit? (iii)How much of each resource will be unused for your solution? 11eab92b_c49a_c15d_99e6_b1b59fc1dffb

The graphical Solution Method can handle problems that involve any number of decision variables.

In linear programming,sensitivity analysis is associated with:

Which of the following is not written in the standard form of a linear programming problem constraint?

A company produces two products (A and B)using three resources (I,II,and III).Each product A requires 1 unit of resource I and 3 units of resource II; and has a profit of $1.Each product B requires 2 units of resource I,3 units of resource II,and 4 units of resource III; and has a profit of $3.Resource I is constrained to 40 units maximum per day; resource II,90 units; and resource III,60 units.What is the constraint for resource II?

A linear programming problem can have multiple optimal solutions.

In graphical linear programming the objective function is:

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.Using the graphical method,what are optimal weekly profits?

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.What is the sugar constraint (in tablespoons)?

If a single optimal solution exists to a graphical LP problem,it will exist at a corner point.

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.For the production combination of 135 Lite and 0 Dark,which resource is "slack" (not fully used)?

A company produces two products (A and B)using three resources (I,II,and III).Each product A requires 1 unit of resource I and 3 units of resource II; and has a profit of $1.Each product B requires 2 units of resource I,3 units of resource II,and 4 units of resource III; and has a profit of $3.Resource I is constrained to 40 units maximum per day; resource II,90 units; and resource III,60 units.What is the objective function?