Sys Ch19

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

True

The equation 5x + 7y = 10 is linear.

True

The term isoprofit line means that all points on the line will yield the same profit.

True

Using the enumeration approach, optimality is obtained by evaluating every coordinate.

False

In linear programming, sensitivity analysis is associated with: (I) the objective function coefficient. (II) right-hand-side values of constraints. (III) the constraint coefficient.

I, II, and III

In graphical linear programming to maximize profit, the objective function is: (I) a family of parallel lines. (II) a family of isoprofit lines. (III) interpolated. (IV) linear.

I, II, and IV only

A linear programming problem can have multiple optimal solutions.

True

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.For the production combination of 600 bagels and 800 croissants, which resource is slack (not fully used)?

flour and sugar

The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150.For the purchase combination 0 king beds and 200 queen beds, which resource is slack (not fully used)?

investment money (only)

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)?

time (only)

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

unlimited.

What combination of x and y will provide a minimum for this problem? Maximize Z = $3x + $15ySubject to: 2x + 4y ≥ 125x + 2y ≥ 10

x = 6, y = 0

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-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the objective function?

$1.00A + $4.00B = Z

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

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

$4x + $2y = $10

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 are optimal weekly profits?

$800

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-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. Which of the following is not a feasible production/sales combination?

100 A and 1,600 B

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 Columbia bean constraint?

12A + 8B ≤ 4,800

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

1A + 2B

A maximization problem is limited by all greater than or equal to constraints.

False

Nonbinding constraints are not associated with the feasible solution space; i.e., they are redundant and can be eliminated from the matrix.

False

The value of an objective function always decreases as it is moved away from the origin.

False

The logistics/operations manager of a mail order house purchases two products for resale: king beds (K) and queen beds (Q). Each king bed costs $500 and requires 100 cubic feet of storage space, and each queen bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each king bed is $300 and for each queen bed is $150.What is the objective function?

Z = $300K + $150Q

In a linear programming problem, the objective function was specified as follows:Z = 2A + 4B + 3CThe optimal solution calls for A to equal 4, B to equal 6, and C to equal 3. It has also been determined that the coefficient associated with A can range from 1.75 to 2.25 without the optimal solution changing. This range is called A's

range of optimality.

A constraint that does not form a unique boundary of the feasible solution space is a

redundant constraint.