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Exam 19: Linear Programming

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Question 51

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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) ?

A) Colombian beans (only)
B) Dominican beans (only)
C) both Colombian beans and Dominican beans
D) neither Colombian beans nor Dominican beans
E) cannot be determined exactly

F) A) and B)
G) None of the above

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Question 52

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

A) 1A + 2B ≤ 3
B) 1A + 2B ≥ 3
C) 1A + 2B = 3
D) 1A + 2B + 3C + 4D ≤ 5
E) 1A + 2B

F) C) and D)
G) B) and C)

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Question 53

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A novice linear programmer is dealing with a three-decision-variable problem. To compare the attractiveness of various feasible decision-variable combinations, values of the objective function at corners are calculated. This is an example of:

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

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?

A linear programming problem can have multiple optimal solutions.

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

The simplex method is a general-purpose LP algorithm that can be used for solving only problems with more than six variables.

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. (A) What combination of A and B will maximize profit? (B) What is the maximum possible profit? (C) How much of each resource will be unused for your solution?

It has been determined that, with respect to resource X, a one-unit increase in availability of X would lead to a $3.50 increase in the value of the objective function. This value would be X's:

For the constraints given below, which point is in the feasible solution space of this minimization problem? $\begin{aligned}14 x + 6 y & \geq 42 \\x + 3 y & \geq 6\end{aligned}$

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

Which of the following choices constitutes a simultaneous solution to these equations? $\begin{array} { l } 3 x + 2 y = 6 \\6 x + 3 y = 12\end{array}$

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

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) ?

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

Once we go beyond two decision variables, typically the ___________ method of linear programming must be used.

Constraints limit the alternatives available to a decision maker; removing constraints adds viable alternative solutions.

Given this problem: Maximize $Z = \$ .30 x + \$ .90 y$ $\begin{array} { l } \text{Subject to:}&2 \mathrm { x } + 3.2 \mathrm { y } \leq 160 \\&4 \mathrm { x } + 2.0 \mathrm { y } \leq 240 \\\mathrm { y } \leq 40\end{array}$ (A) Solve for the quantities of x and y which will maximize Z. (B) What is the maximum value of Z?

Which of the following choices constitutes a simultaneous solution to these equations? $\begin{array} { l } 3 \mathrm { x } + 4 \mathrm { y } = 10 \\5 \mathrm { x } + 4 \mathrm { y } = 14\end{array}$