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Exam 19: Linear Programming

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Question 41

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

A) True
B) False

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Question 42

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In a linear programming problem, the objective function was specified as follows: Z = 2A + 4B + 3C The 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:

A) range of optimality.
B) range of feasibility.
C) shadow price.
D) slack.
E) surplus.

F) B) and D)
G) A) and E)

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Question 43

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

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 assembly time constraint (in hours) ?

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 III?

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. Which of the following is not a feasible production combination?

In a linear programming problem involving maximization, at least one constraint must be of the __________ type.

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

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?

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?

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?

Solve the following linear programming problem: Minimize $Z = \$ 7 x + \$ 7 y$ $\begin{array} { l } \text{Subject to:}&14 x + 4 y \geq 280 \\&30 x + 70 y \geq 2,100 \\&y \leq 60 \\&y \geq 10\end{array}$

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

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. Which of the following is not a feasible production combination?

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

A maximization problem may be characterized by all greater than or equal to constraints.

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S) . Two resources are constrained: production time (T) , of which she has at most 12 hours per day; and carbonated water (W) , of which she can get at most 1,500 gallons per day. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case. What is the production time constraint (in minutes) ?

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

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

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