Exam 2: Introduction to Optimization and Linear Programming

Solve the following LP problem graphically using level curves. MAX: ^{5 X}₁ ^{+ 3 X}₂ Subject to: ^{2 X}₁ ^{− 1 X}₂ ^{≤ 2} 6 X₁ + 6 X₂ ≥ 12 1 X₁ + 3 X₂ ≤ 5 X₁,X₂ ≥ 0

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?

Solve the following LP problem graphically by enumerating the corner points. MIN: ^{8 X}₁ ^{+ 5 X}₂ Subject to: ^{6 X}₁ ^{+ 7 X}₂ ^{≥ 84} X₁ ≥ 4 X₂ ≥ 6 X₁,X₂ ≥ 0

In a mathematical formulation of an optimization problem,the objective function is written as z=2x₁+3x₂.Then:

Some resources i.e.meat and dairy products,pharmaceuticals,a can of paint)are perishable.This means that once a package

A redundant constraint is one which

Mathematical programming is referred to as

A common objective in the product mix problem is

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

The desire to maximize profits is an example of an)

Solve the following LP problem graphically by enumerating the corner points. MIN: ^{8 X}₁ ^{+ 3 X}₂ Subject to: ^X₂ ^{≥ 8} 8 X₁ + 5 X₂ ≥ 80 3 X₁ + 5 X₂ ≥ 60 X₁,X₂ ≥ 0

Solve the following LP problem graphically by enumerating the corner points. MAX: ^{2 X}₁ ^{+ 7 X}₂ Subject to: ^{5 X}₁ ^{+ 9 X}₂ ^{≤ 90} 9 X₁ + 8 X₂ ≤ 144 X₂ ≤ 8 X₁,X₂ ≥ 0

If constraints are added to an LP model the feasible solution space will generally

Solve the following LP problem graphically using level curves. MIN: ^{5 X}₁ ^{+ 7 X}₂ Subject to: ^{4 X}₁ ^{+ 1 X}₂ ^{≥ 16} 6 X₁ + 5 X₂ ≥ 60 5 X₁ + 8 X₂ ≥ 80 X₁,X₂ ≥ 0

Most individuals manage their individual retirement accounts IRAs)so they

Which of the following is the general format of an objective function?

The constraint for resource 1 is 5 X₁ + 4 X₂ ≥ 200.If X₁ = 40 and X₂ = 20,how many additional units,if any,of resource 1 are employed above the minimum of 200?

Suppose that a constraint 2x₁+3x₂ ≥ 600 is binding.Then,a constraint 4x₁+6x₂ ≥ 1,800 is

A common objective when manufacturing printed circuit boards is

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.