Chapter 19 (FINAL EXAM)

Which of the following is not a component of the structure of a linear programming model?

environmental uncertainty

Profit maximization could be an objective of an LP problem; but cost minimization cannot be the objective of an LP problem.

false

The equation 3xy = 9 is linear.

false

The region which satisfies all of the constraints in graphical linear programming is called the

feasible solution space

A linear programming problem can have multiple optimal solutions

true

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

true

LP problems must have a single goal or objective specified.

true

The feasible solution space only contains points that satisfy all constraints.

true

What combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: 2x + 4y ≤ 12 5x + 2y ≤ 10

x= 0 , y=3

For a linear programming problem with the following constraints, which point is in the feasible solution space assuming this is a maximization problem? 14x+6y≤42x−y≤3

x= 2 , y= 1

Which of the following choices constitutes a simultaneous solution to these equations? 3x+4y=105x+4y=14

x= 2 , y= 1

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

identifying the decision variables

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 objective function?

$2A + $1B= Z

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)?

$2B + $4C <_4,800

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. What is the objective function?

$3L + $2D= Z

Which objective function has the same slope as this one: $4x + $2y = $20?

$4x + $2y= $10

Which of the following could not be a linear programming problem constraint?

1A + 2B (no right-hand value)

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 $.40; and for a box of Classic crackers, $.50. What is the constraint for sugar?

2D + 3C <_ 4,800

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

Z= 1A + 2B + 3C + 4D

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

linear programming