Exam 2: Introduction to Optimization and Linear Programming

A company makes two products,X₁ and X₂.They require at least 20 of each be produced.Which set of lower bound constraints reflect this requirement?

Solve the following LP problem graphically by enumerating the corner points. MAX: ^{4 X}₁ ^{+ 3 X}₂ Subject to: ^{6 X}₁ ^{+ 7 X}₂ ^{≤ 84} X₁ ≤ 10 X₂ ≤ 8 X₁,X₂ ≥ 0

The constraint for resource 1 is 5 X₁ + 4 X₂ ≤ 200.If X₁ = 20,what it the maximum value for X₂?

A manager has only 200 tons of plastic for his company.This is an example of an)

A mathematical programming application employed by a shipping company is most likely

For an infeasible problem,the feasible region:

The number of units to ship from Chicago to Memphis is an example of an)

Solve the following LP problem graphically using level curves. MAX: ^{7 X}₁ ^{+ 4 X}₂ Subject to: ^{2 X}₁ ^{+ X}₂ ^{≤ 16} X₁ + X₂ ≤ 10 2 X₁ + 5 X₂ ≤ 40 X₁,X₂ ≥ 0

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.

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is

The following linear programming problem has been written to plan the production of two products.The company wants to maximize its profits. X₁ = number of product 1 produced in each batch X₂ = number of product 2 produced in each batch MAX: ^{150 X}₁ ^{+ 250 X}₂ Subject to: ^{2 X}₁ ^{+ 5 X}₂ ^{≤ 200} 3 X₁ + 7 X₂ ≤ 175 X₁,X₂ ≥ 0 How much profit is earned per each unit of product 2 produced?

Limited resources are modeled in optimization problems as

A facility produces two products and wants to maximize profit.The objective function to maximize is z=350x₁+300x₂.The number 350 means that:

What most motivates a business to be concerned with efficient use of their resources?

The third step in formulating a linear programming problem is

What are the three common elements of an optimization problem?

Bob and Dora Sweet wish to start investing $1,000 each month.The Sweets are looking at five investment plans and wish to maximize their expected return each month.Assume interest rates remain fixed and once their investment plan is selected they do not change their mind.The investment plans offered are: Fidelity 9.1% return per year Optima 16.1% return per year CaseWay 7.3% return per year Safeway 5.6% return per year National 12.3% return per year Since Optima and National are riskier,the Sweets want a limit of 30% per month of their total investments placed in these two investments.Since Safeway and Fidelity are low risk,they want at least 40% of their investment total placed in these investments. Formulate the LP model for this problem.

Solve the following LP problem graphically using level curves. MIN: ^{8 X}₁ ^{+ 12 X}₂ Subject to: ^{2 X}₁ ^{+ 1 X}₂ ^{≥ 16} 2 X₁ + 3 X₂ ≥ 36 7 X₁ + 8 X₂ ≥ 112 X₁,X₂ ≥ 0

The following linear programming problem has been written to plan the production of two products.The company wants to maximize its profits. X₁ = number of product 1 produced in each batch X₂ = number of product 2 produced in each batch MAX: ^{150 X}₁ ^{+ 250 X}₂ Subject to: ^{2 X}₁ ^{+ 5 X}₂ ^{≤ 200} 3 X₁ + 7 X₂ ≤ 175 X₁,X₂ ≥ 0 How many units of resource one the first constraint)are used if the company produces 10 units of product 1 and 5 units of product 2?

The constraints of an LP model define the