ECON 3300 Exam Review Ch. 3 Quizzes

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25. The LP formulation that maximizes week profit shown below. MAX 15A +18B + 25 C s.t. 2A + 2.5B + 3C ≤ 300 20A + 30B + 45C ≤ 3750 10A + 14B + 18C ≤ 3000 The solution from QM for Windows is show below. Billy's accountant made an error, and the budget has been reduced from $3000 to $2500. Billy's profit will go down by:

$0.

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia feels that her prices are too low, particularly for her eggs. How much would her profit have to increase on the eggs before it is profitable for her to make and sell eggs?

$1.00

Given the following linear program that maximizes revenue: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What is the maximum revenue at the optimal solution?

$160

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally?

$29.00

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25. The LP formulation that maximizes week profit shown below. MAX 15A +18B + 25 C s.t. 2A + 2.5B + 3C ≤ 300 20A + 30B + 45C ≤ 3750 10A + 14B + 18C ≤ 3000 The solution from QM for Windows is show below. If one of Billy's machines breaks down, it usually results in about 6 hours of downtime. When this happens, Billy's profits are reduced by:

$35

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the optimal weekly profit?

$800

Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. How should the requirement that the bar setups should change at least every other day but no more than twice per day?

1 Bar ≥ 7 1 Bar ≤ 28

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: The optimal quantity of the three products and resulting revenue for Taco Loco is:

1.45 Z, 8.36 Y, and 0 Z for $129.09.

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix?

17.78 to 30 pounds

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z?

28.73

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. Which of the following is not a feasible solution?

300 L and 200 D

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. What is the appropriate constraint for the budget?

900 Bar + 1500 Food + 5,000 Excursion ≤ 150,000

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

A + B ≤ -3

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia can obtain an additional 10 hours of kiln capacity free of charge from a friend. If she did this, how would her profits be affected?

Cannot tell from the information provided.

Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. Here's a lovely portion of the sensitivity report for the constraints. Which of these conclusions is reasonable? Final Shadow Constraint Cell Name Value Price R.H. Side $E$10 Bar/Food 0 1560 0 $E$11 Budget 150000 3.4 150000 $E$6 Excursions 24.24 0 5 $E$7 Restaurant 12 -1660 12 $E$8 Bar Low 12 0 7 $E$9 Bar High 12 0 28

Captain Stubing should exhaust his Budget.

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. What is the appropriate constraint for the requirement that there should be at least one different bar setup for every different type of food?

Food - Bar ≤ 0

Using this snippet of the sensitivity report for variable cells, which of these conclusions is best? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$13 A 9 0 5 1E+30 1.25 $C$13 B 0 -2 6 2 1E+30 $D$13 C 0 -2 1 2 1E+30

Insisting that one additional unit of B, be included in the model will reduce the profit by $2.

Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. Here's a portion of the sensitivity analysis for the constraints. Which of these statements is best? Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$10 Bar/Food 0 1560 0 5 16 $E$11 Budget 150000 3.4 150000 1E+30 96200 $E$6 Excursions 24.24 0 5 19.24 1E+30 $E$7 Restaurant 12 -1660 12 16 5

If the budget rises to $150,001, then the optimal mix will result in an increased revenue of $3.40.

Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. Here's the sensitivity report for the decision variables. Which of these conclusions is correct? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$2 Bar 12 0 1500 1560 1E+30 $C$2 Cuisine 12 0 5000 1660 1E+30 $D$2 Excursion 24.24 0 17000 1E+30 3458.333333

It doesn't matter how much money they make on excursions, the optimal answer will continue to be 24.24 of them.

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Which additional resources would you recommend that Aunt Anastasia try to obtain?

Kiln

Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. What should Captain Stubing's objective function be?

Max Z = 1500 Bar + 5000 Food + 17000 Excursion

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia's available hours for paint and seal have fallen from 80 hours to 60 hours because of other commitments. How will this affect her profits?

Profits will not change.

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Suppose the charitable organization contacted Aunt Anastasia and told her that they had underestimated the amount of rabbits they needed. Instead of 25 rabbits, they need 35. How would this affect Aunt Anastasia's profits?

Profits would decrease by $5.

Using this snippet of the sensitivity report for constraints, which of these conclusions is best? Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$15 One 45 1 45 1.666666667 45 $E$16 Two 54 0 56 1E+30 2 $E$17 Three 27 0 67 1E+30 40 $E$18 Four 72 0 78 1E+30 6

Taking away four units of One will lower the objective function value by four.

Ch03 - The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. Based on the variable cells sensitivity report, what conclusion is best? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$2 Bar 12 0 1500 1560 1E+30 $C$2 Cuisine 12 0 5000 1660 1E+30 $D$2 Excursion 24.24 0 17000 1E+30 3458.333333

The optimal value for the objective function is $490,080

A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 300 minutes, providing two additional machine hours will result in:

a different product mix, different total profit.

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table: Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program. B = number of baskets produced E = number of eggs produced R = number of rabbits produced MAX 2.5B + 1.5E + 2R s.t. 0.5B + 0.333E + 0.25R ≤ 20 B + E + R ≤ 50 0.25B + 0.333E + 0.75R ≤ 80 R ≥ 25 The Excel solution and the answer and sensitivity report are shown below. The Answer Report: The Sensitivity Report: Aunt Anastasia is planning for next spring, and she is considering making only two products. Based on the results from the linear program, which two products would you recommend that she make?

baskets and rabbits

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: The local cheese vendor offers to sell Taco Loco 200 pounds of cheese for these three products. Taco Loco should:

buy 46 pounds or less of cheese for $1.45 or less.

For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________.

improvement, resource

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25. The LP formulation that maximizes week profit shown below. MAX 15A +18B + 25 C s.t. 2A + 2.5B + 3C ≤ 300 20A + 30B + 45C ≤ 3750 10A + 14B + 18C ≤ 3000 The solution from QM for Windows is show below. Billy has decided that he can raise the price on the Curious t-shirt by 10% without losing sales. If he raises the price, his profits will:

increase by $125.

Billy's Blues sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 20 minutes of labor, and costs $10. Brand Bling requires 2.5 minutes of machine time and 30 minutes of labor, and costs $14 to produce. Brand Curious requires 3 minutes of machine time and 45 minutes of labor, and costs $18 to produce. There are 300 machining hours available per week, 3750 labor hours, and he has a budget of $3000. Brand Astro sells for $15, Brand Bling for $18, and Brand Curious for $25. The LP formulation that maximizes week profit shown below. MAX 15A +18B + 25 C s.t. 2A + 2.5B + 3C ≤ 300 20A + 30B + 45C ≤ 3750 10A + 14B + 18C ≤ 3000 The solution from QM for Windows is show below. If Billy could acquire more of any resource, which would it be?

machining time

Sensitivity analysis is the analysis of the effect of ________ changes on the ________.

parameter, optimal solution

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:

same product mix, different total profit.

A shadow price reflects which of the following in a maximization problem?

the marginal gain in the objective that would be realized by adding one unit of a resource

The production manager for Beer etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. If the production manager decides to produce of 400 bottles of light beer and 0 bottles of dark beer, it will result in slack of:

wheat only

For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint:

will have a value of zero.

Given the following linear programming problem: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What would be the values of x and y that will maximize revenue?

x = 0; y = 8

For the constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y ≤ 42 (2) x + 3y ≥ 6

x = 1; y = 2

Use the constraints given below and determine which of the following points is feasible. (1) 14x + 6y ≤ 42 (2) x - y ≤ 3

x = 1; y = 4

What combination of x and y is a feasible solution that minimizes the value of the objective function? Min Z = 3x + 15y (1) 2x + 4y ≥ 12 (2) 5x + 2y ≥10

x = 5; y = 0

For a resource constraint, either its slack value must be ________ or its shadow price must be ________.

zero, zero