Question 1

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited so at most 8 will be produced.
a.Formulate the LP model for this problem.
b.Solve the problem using the graphical method.

Accepted Answer

The answer of Jones Furniture Company produces beds and desks...

Question 2

The Happy Pet pet food company produces dog and cat food. Each food is comprised of meat, soybeans and fillers. The company earns a profit on each product but there is a limited demand for them. The pounds of ingredients required and available, profits and demand are summarized in the following table. The company wants to plan their product mix, in terms of the number of bags produced, in order to maximize profit.
  
a.Formulate the LP model for this problem.
b.Solve the problem using the graphical method.

Accepted Answer

The answer of The Happy Pet pet food company produces...

Question 3

Solve the following LP problem graphically by enumerating the corner points.

Accepted Answer

The answer of Solve the following LP problem graphically by...

Question 4

When do alternate optimal solutions occur in LP models?
A)When a binding constraint is parallel to a level curve.
B)When a non-binding constraint is perpendicular to a level curve.
C)When a constraint is parallel to another constraint.
D)Alternate optimal solutions indicate an infeasible condition.

Accepted Answer

Chapter says level curve sits on feasible region edge, which implies parallel

Question 5

Which of the following special conditions in an LP model represent potential errors in the mathematical formulation?
A)Alternate optimum solutions and infeasibility.
B)Redundant constraints and unbounded solutions.
C)Infeasibility and unbounded solutions.
D)Alternate optimum solutions and redundant constraints.

Accepted Answer

The answer of Which of the following special conditions in...

Question 6

Solve the following LP problem graphically by enumerating the corner points.

Accepted Answer

The answer of Solve the following LP problem graphically by...

Question 7

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Question 8

The Big Bang explosives company produces customized blasting compounds for use in the mining industry. The two ingredients for these explosives are agent A and agent B. Big Bang just received an order for 1400 pounds of explosive. Agent A costs $5 per pound and agent B costs $6 per pound. The customer's mixture must contain at least 20% agent A and at least 50% agent B. The company wants to provide the least expensive mixture which will satisfy the customers requirements.
a.Formulate the LP model for this problem.
b.Solve the problem using the graphical method.

Accepted Answer

The answer of The Big Bang explosives company produces customized...

Question 9

A redundant constraint is one which
A)plays no role in determining the feasible region of the problem.
B)is parallel to the level curve.
C)is added after the problem is already formulated.
D)can only increase the objective function value.

Accepted Answer

A redundant constraint does not affect the feasible region of the problem and can be removed without changing the optimal solution or the feasible region. Therefore, it is irrelevant to the optimization problem and can be considered as unnecessary.

Question 10

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Question 11

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem? 
A)A
B)B
C)C
D)D
E)E

Accepted Answer

The answer of This graph shows the feasible region (defined...

Question 12

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Question 13

When the objective function can increase without ever contacting a constraint the LP model is said to be
A)infeasible.
B)open ended.
C)multi-optimal.
D)unbounded.

Accepted Answer

If the objective function can increase without ever contacting a constraint, then the LP model is unbounded. This means that there is no maximum value for the objective function, and the optimal solution goes towards infinity.

Question 14

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be
A)infeasible.
B)open ended.
C)multi-optimal.
D)unbounded.

Accepted Answer

If there is no feasible solution that can satisfy all the constraints in an LP model, the problem is said to be infeasible.

Question 15

The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces a limited demand. There are a limited number of wiring, assembly and inspection hours available next month. The data for this problem is summarized in the following table.  
a.Formulate the LP model for this problem.
b.Solve the problem using the graphical method.

Accepted Answer

The answer of The Byte computer company produces two models...

Question 16

Solve the following LP problem graphically by enumerating the corner points.

Accepted Answer

The answer of Solve the following LP problem graphically by...

Question 17

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Question 18

Solve the following LP problem graphically by enumerating the corner points.

Accepted Answer

The answer of Solve the following LP problem graphically by...

Question 19

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Question 20

Jim's winery blends fine wines for local restaurants. One of his customers has requested a special blend of two burgundy wines, call them A and B. The customer wants 500 gallons of wine and it must contain at least 100 gallons of A and be at least 45% B. The customer also specified that the wine have an alcohol content of at least 12%. Wine A contains 14% alcohol while wine B contains 10%. The blend is sold for $10 per gallon. Wine A costs $4 per gallon and B costs $3 per gallon. The company wants to determine the blend that will meet the customer's requirements and maximize profit.
a.Formulate the LP model for this problem.
b.Solve the problem using the graphical method.
c.How much profit will Jim make on the order?

Accepted Answer

The answer of Jim's winery blends fine wines for local...

Quiz 2: Introduction to Optimization and Linear Programming

Solve the following LP problem graphically by enumerating the corner points.

When do alternate optimal solutions occur in LP models?

Which of the following special conditions in an LP model represent potential errors in the mathematical formulation?

Solve the following LP problem graphically by enumerating the corner points.

Solve the following LP problem graphically using level curves.

A redundant constraint is one which

Solve the following LP problem graphically using level curves.

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?

Solve the following LP problem graphically using level curves.

When the objective function can increase without ever contacting a constraint the LP model is said to be

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Solve the following LP problem graphically by enumerating the corner points.

Solve the following LP problem graphically using level curves.

Solve the following LP problem graphically by enumerating the corner points.

Solve the following LP problem graphically using level curves.