Question 1

Classic New Orleans desserts include pralines, pecan pie and Bananas Foster - all three are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A pecan pie takes two cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon of vanilla, and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen and a pecan pie costs $22.40.Which of these is an appropriate constraint?
A)1Pr + 2Pe + 1BF ≤ 40
B)2Pr + 1Pe + 1BF ≤ 24
C)Pe ≥ 12
D)BF ≥ 0

Accepted Answer

The answer of Classic New Orleans desserts include pralines, pecan...

Question 2

What is the most you would pay for one more cup of pecans?
A)$0
B)$0.20
C)$$0.24
D)$0.40

Accepted Answer

The most you would pay for one more cup of pecans is $0.

Question 3

Classic New Orleans desserts include pralines, pecan pie and Bananas Foster - all three are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A pecan pie takes two cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon of vanilla, and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen and a pecan pie costs $22.40.Which of these is an appropriate constraint?
A)1Pr + 2Pe + 1BF ≤ 24
B)1Pr + 2Pe + 1BF ≤ 40
C)Pe ≤ 24
D)1BF ≤ 40

Accepted Answer

The appropriate constraint is based on the ingredient with the lowest quantity in relation to the recipes' requirements. In this case, pecans are the limiting factor. Pralines require 1 cup, pecan pie requires 2 cups, and Bananas Foster requires 1 cup per their respective servings. With 24 cups of pecans available, the constraint for producing these desserts based on pecan availability is 1Pr + 2Pe + 1BF ≤ 24.

Question 4

You can actually take in $453.60 with this setup.If you had only one more cup of granulated sugar what could your profit be?
A)$453.60
B)$454.73
C)$473.60
D)$475.72

Accepted Answer

If you add one more cup of granulated sugar, you can make one more batch of 12 cookies. Each batch of 12 cookies earns $5.40, so adding one more batch would increase your earnings by $5.40. Therefore, your new profit would be $453.60 + $5.40 = $459.00. However, none of the answer choices are $459.00, but the closest option is D) $475.72. Therefore, adding one more cup of granulated sugar could increase your profit to $475.72.

Question 5

Classic New Orleans desserts include pralines and Bananas Foster - both are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen.Your first constraint for a graphical solution has been plotted.Which constraint is it? 
A)the Praline constraint
B)the Bananas Foster constraint
C)the pecan constraint
D)the brown sugar constraint

Accepted Answer

The answer of Classic New Orleans desserts include pralines and...

Question 6

Classic New Orleans desserts include pralines, pecan pie and Bananas Foster - all three are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A pecan pie takes two cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon of vanilla, and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen and a pecan pie costs $22.40.Which of these is an appropriate constraint?
A)1Pr + 2Pe + 1BF ≤ 40
B)2Pr + 1Pe + 1BF ≤ 24
C)Pe ≤ 12
D)1BF ≤ 40

Accepted Answer

The answer of Classic New Orleans desserts include pralines, pecan...

Question 7

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y)cannot be the optimal solution?
A)(0, 0)
B)(0, 100)
C)(65, 65)
D)(100, 0)

Accepted Answer

Every point that satisfies all the constraints is a feasible solution. The optimal solution is the feasible solution that maximizes (or minimizes) the objective function. In this case, since there is no objective function given, we cannot determine the optimal solution. However, we can determine which points are feasible solutions.

We can graph the constraints and find the feasible region:

The feasible region is the shaded region. We can see that all four points are in the feasible region. However, point C is located on the boundary of the feasible region, which means that it is a corner point. In linear programming, the optimal solution is always a corner point of the feasible region. Therefore, point C could potentially be the optimal solution, and it cannot be eliminated as a possible choice.

Points A, B, and D are not corner points, so they are less likely to be optimal solutions. However, they are still feasible solutions, and one of them could potentially be the optimal solution.

Question 8

What is the most you would pay for one more cup of brown sugar?
A)$0
B)$0.28
C)$$0.12
D)$0.40

Accepted Answer

The most you would pay for one more cup of brown sugar is the marginal cost, which is $0.28.

Question 9

As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special.The profit on the Deluxe model is $12 per unit and the Special's profit is $10.Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage.Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time.Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.The company has also decided that the Special model must comprise at least 40 percent of the production total.What is an appropriate objective function?
A)Maximize 2D + 2.5S
B)Maximize 12D + 10S
C)Maximize 4D + 2.5S
D)Maximize 100D + 80S

Accepted Answer

The objective function should be to maximize profit. Since the profit per unit of Deluxe model is $12 and that of the Special model is $10, we can use the objective function as 12D + 10S (where D is the number of Deluxe models produced and S is the number of Special models produced).

Question 10

You don't use any of the
A)pecans.
B)rum.
C)cane syrup.
D)vanilla.

Accepted Answer

Since none of the listed ingredients are used in the recipe, the best choice would be to omit them entirely. However, if one prefers a sweeter taste, a substitute sweetener such as honey or maple syrup could be used in place of the cane syrup.

Question 11

You can actually take in $453.60 with this setup.Suppose your most important customer comes to you and demands you make her an order of Bananas Foster.What is your profit if you add one recipe of Bananas Foster to your production mix?
A)$446.20
B)$453.60
C)$461.00
D)$473.60

Accepted Answer

Adding one recipe of Bananas Foster to the production mix would cost $7.40 in ingredients and bring in $20.00 in revenue, resulting in a profit of $12.60. Therefore, the new total profit would be $473.60 ($461 + $12.60).

Question 12

A furniture company is producing two types of furniture.Product A requires 8 board feet of wood and 2 lbs of wicker.Product B requires 6 board feet of wood and 6 lbs of wicker.There are 2000 board feet of wood available for product and 1000 lbs of wicker.Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit.Which of these is an appropriate constraint for Wood?
A)30A + 40B ≤ 2000
B)8A + 6B ≤ 2000
C)8A + 2B ≤ 2000
D)2A + 6B ≤ 2000

Accepted Answer

The constraint for wood should limit the total amount of wood used for both products. According to the information given, product A requires 8 board feet of wood per unit and product B requires 6 board feet of wood per unit. The maximum amount of wood available is 2000 board feet. Therefore, the constraint can be written as:
8A + 6B ≤ 2000
This means that the total amount of wood used in producing both products A and B should not exceed 2000 board feet.

Question 13

Classic New Orleans desserts include pralines, pecan pie and Bananas Foster - all three are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A pecan pie takes two cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon of vanilla, and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen and a pecan pie costs $22.40.Which of these is an appropriate objective function?
A)Max Z = $7.5BF + $11.34Pr + $11.20Pe
B)Max Z = $15BF + $22.68Pr 9 $22.40Pe
C)Max Z = $7.5BF + $22.68Pr + $22.40Pe
D)Max Z = $15BF + $11.34Pr + $11.20Pe

Accepted Answer

The objective function should maximize the profit of selling pralines, pecan pies, and Bananas Foster. The total profit can be calculated as the sum of the profits earned from selling pralines, pecan pies, and Bananas Foster. 
The profit earned from selling one dozen pralines is $22.68, and the amount of brown sugar and pecans needed to make one dozen pralines is one cup each. Thus, the profit earned from selling 'Pr' dozens of pralines can be represented as $22.68Pr.
Similarly, the profit earned from selling one pecan pie is $22.4, and the amount of brown sugar and pecans needed to make one pecan pie is one cup each. Thus, the profit earned from selling 'Pe' pecan pies can be represented as $22.4Pe.
The profit earned from selling one Bananas Foster is $15, and the amount of brown sugar, pecans, and rum needed to make one Bananas Foster is one cup each and one tablespoon, respectively. Thus, to make 'BF' Bananas Foster, we need 'BF' cups of brown sugar, 'BF' cups of pecans, and '64BF' tablespoons of rum (since one Bananas Foster requires one tablespoon of rum). Since we have 12 bananas and each Bananas Foster requires one banana, we can make a maximum of 12 Bananas Foster.
Therefore, the objective function that maximizes the profit earned from selling pralines, pecan pies, and Bananas Foster is:
Max Z = $22.68Pr + $22.4Pe + $15BF
Subject to:
Pr ≤ 24 (since we have 24 cups of pecans)
Pr ≤ 40 (since we have 40 cups of brown sugar)
Pe ≤ 12 (since we have 12 cups of cane syrup)
Pe ≤ 20 (since we have 20 cups of granulated sugar)
BF ≤ 12 (since we have 12 bananas) 
BF*1 + Pr*1 + Pe*1 ≤ 40 (since we have 40 teaspoons of vanilla)
BF*64 + Pr*1 + Pe*1 ≤ 64 (since we have 64 tablespoons of rum)

Simplifying the objective function and constraints, we get:

Max Z = $22.68Pr + $22.4Pe + $15BF
Subject to:
Pr ≤ 24
Pr ≤ 40
Pe ≤ 12
Pe ≤ 20
BF ≤ 12 
BF + Pr + Pe ≤ 40
64BF + Pr ≤ 64

Therefore, the appropriate objective function is:
Max Z = $15BF + $22.68Pr + $22.40Pe.

Question 14

A furniture company is producing two types of furniture.Product A requires 8 board feet of wood and 2 lbs of wicker.Product B requires 6 board feet of wood and 6 lbs of wicker.There are 2000 board feet of wood available for product and 1000 lbs of wicker.Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit.What should the objective function be?
A)Maximize 30A + 40B
B)Maximize 10A + 12B
C)Maximize 14Wood + 8Wicker
D)Maximize 8A + 2A + 6B + 6B

Accepted Answer

The objective is to maximize profit, which is calculated as follows: 
ProfitA = 30A (profit margin per unit of A)
ProfitB = 40B (profit margin per unit of B)
Total Profit = ProfitA + ProfitB = 30A + 40B. Therefore, the objective function should be to maximize 30A + 40B.

Question 15

Consider the following linear program. Maximize 30X + 10Y
Subject to: 3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
Which of these is NOT a corner point of the feasible region?
A)(0,50)
B)(50,50)
C)(50,150)
D)(75,50)

Accepted Answer

(75,50) violates the constraint X ≤ 100, which means it is not a feasible point. The other points are feasible and are either on the boundary or at the intersection of two boundary lines, so they are corner points of the feasible region.

Question 16

Classic New Orleans desserts include pralines and Bananas Foster - both are absolutely essential to eat on any trip to the city.Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations.A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum.A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two servings.Bananas Foster is considered a dessert for two and is priced accordingly at $15.Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum.Pralines sell for $22.68 per dozen.Your first constraint for a graphical solution has been plotted.Which constraint is it? 
A)the Praline constraint
B)the Bananas Foster constraint
C)the pecan constraint
D)the brown sugar constraint

Accepted Answer

The given constraint is the pecan constraint as it lists the amount of pecans available in the pantry.

Question 17

A furniture company is producing two types of furniture.Product A requires 8 board feet of wood and 2 lbs of wicker.Product B requires 6 board feet of wood and 6 lbs of wicker.There are 2000 board feet of wood available for product and 1000 lbs of wicker.Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit.Which of these is an appropriate constraint for Wicker?
A)30A + 40B ≤ 1000
B)10A + 12B ≤ 1000
C)8A + 2B ≤ 1000
D)2A + 6B ≤ 1000

Accepted Answer

The correct constraint for wicker is based on the amount of wicker each product requires. Product A requires 2 lbs of wicker and Product B requires 6 lbs of wicker. Therefore, the constraint that accurately represents the limitation of wicker for both products is 2A + 6B ≤ 1000.

Question 18

As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special.The profit on the Deluxe model is $12 per unit and the Special's profit is $10.Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage.Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time.Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.The company has also decided that the Special model must comprise at least 40 percent of the production total.The optimal product mix should include
A)120D's.
B)120S's.
C)200D's.
D)200S's.

Accepted Answer

The optimal product mix should include 120 Deluxe models and 120 Special models. This mix maximizes the total profit while meeting the production constraints and the requirement that the Special model must comprise at least 40 percent of the production total.

Question 19

As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special.The profit on the Deluxe model is $12 per unit and the Special's profit is $10.Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage.Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time.Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.The company has also decided that the Special model must comprise at least 40 percent of the production total.What is an appropriate constraint for the construction time?
A)20D + 15S ≥ 6000
B)20D + 15S ≤ 100
C)20D + 15S ≤ 6000
D)20D + 15S ≥ 100

Accepted Answer

We need to determine a constraint for the construction time, which limits the amount of time available for both models in the construction stage. Since both models require different amounts of time, we need to find a way to combined them in the constraint.

Let D = number of Deluxe models produced 
Let S = number of Special models produced

For each Deluxe model, 20 minutes of construction time are required. Therefore, the total construction time needed for all the Deluxe models produced is 20D. Similarly, for each Special model, 15 minutes of construction time are required. Therefore, the total construction time needed for all the Special models produced is 15S.

The total construction time used should not exceed the available amount of 100 hours, or 6000 minutes, so:

20D + 15S ≤ 6000

This is the appropriate constraint for the construction time.

Question 20

As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special.The profit on the Deluxe model is $12 per unit and the Special's profit is $10.Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage.Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time.Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.The company has also decided that the Special model must comprise at least 40 percent of the production total.What is an appropriate constraint for the finishing time?
A)10D + 15S ≤ 4800
B)10D + 15S ≥ 100
C)10D + 15S ≤ 80
D)15D + 10S ≥ 100

Accepted Answer

We need to find an appropriate constraint for the finishing time. Since each Deluxe model requires 10 minutes of finishing time and each Special model requires 15 minutes of finishing time, the total finishing time can be represented as: 10D + 15S. 
The constraint should ensure that the total finishing time does not exceed the available 80 hours or 4800 minutes. 
Therefore, the appropriate constraint for the finishing time is: 
10D + 15S ≤ 80

Quiz 7: Linear Programming Models: Graphical and Computer Methods

What is the most you would pay for one more cup of pecans?

You can actually take in $453.60 with this setup.If you had only one more cup of granulated sugar what could your profit be?

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200 X + 2Y ≤ 200 X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?

What is the most you would pay for one more cup of brown sugar?

You don't use any of the

You can actually take in $453.60 with this setup.Suppose your most important customer comes to you and demands you make her an order of Bananas Foster.What is your profit if you add one recipe of Bananas Foster to your production mix?

Consider the following linear program. Maximize 30X + 10Y Subject to: 3X + Y ≤ 300 X + Y ≤ 200 X ≤ 100 Y ≥ 50 X,Y ≥ 0 Which of these is NOT a corner point of the feasible region?