Exam 6: B: Process Design and Facility Layout

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

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)?

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?

Determine the amounts of x and y that will minimize cost.What is the minimum cost these amounts will yield? Minimize Z = $7x + $7y Subject to: 14x + 4y³ 280 30x + 70y³ 2,100 y ≤ 60 y³ 10

A change in the value of an objective function coefficient does not change the optimal solution.

Consider the graphical linear programming problem below: Maximize Z = $15X + $20y Subject to: (i)8x + 5y ≤ 40 (ii).4x + y ≥ 4 Solve the values of x and y that will maximize revenue.What revenue will result?

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 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?

For the constraints given below,which point is in the feasible solution space of this maximization problem? (1)14x + 6y ≤ 42 (2)x - y ≤ 3

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 optimum production combination and its profits?

Slack or surplus is associated with a binding constraint.

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

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.For the production combination of 800 boxes of Deluxe and 600 boxes of Classic,which resource is slack (not fully used)?

An objective function represents a family of parallel lines.

The logical approach,from beginning to end,for assembling a linear programming model begins with:

The feasible solution space is the set of all feasible combinations of decision variables as defined by only binding constraints.

LP problems must have a single goal or objective specified.

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.What is the Dominican bean constraint?

The term "range of optimality" refers to a constraint's right-hand side quantity.