Exam 2: Introduction to Optimization and Linear Programming

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.

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.

Solve the following LP problem graphically using level curves.

The objective function for a LP model is 3 X₁ + 2 X₂. If X₁ = 20 and X₂ = 30, what is the value of the objective function?

The constraints of an LP model define the

Linear programming problems have

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

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

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?

The desire to maximize profits is an example of a(n)

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

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 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?

The first step in formulating a linear programming problem is

Mathematical programming is referred to as

The third step in formulating a linear programming problem is

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

Joey Koons runs a small custom computer parts company. As a sideline he offers customized and pre-built computer system packages. In preparation for the upcoming school year, he has decided to offer two custom computer packages tailored for what he believes are current student needs. System A provides a strong computing capability at a reasonable cost while System B provides a much more powerful computing capability, but at a higher cost. Joey has a fairly robust parts inventory but is concerned about his stock of those components that are common to each proposed system. A portion of his inventory, the item cost, and inventory level is provided in the table below. The requirements for each system are provided in the following table: Each system requires assembly, testing and packaging. The requirements per system built and resources available are summarized in the table below. Joey is uncertain about product demand. In the past he has put together similar types of computer packages but his sales results vary. As a result is unwilling to commit all his in-house labor force to building the computer packages. He is confident he can sell all he can build and is not overly concerned with lost sales due to stock-outs. Based on his market survey, he has completed his advertising flyer and will offer System A for $ 1250 and will offer system B for $ 2325. Joey now needs to let his workers know how many of each system to build and he wants that mix to maximize his profits. Formulate an LP for Dave's problem. Solve the model using the graphical method. What is Dave's preferred product mix? What profit does Dave expect to make from this product mix?

Solve the following LP problem graphically using level curves.

Solve the following LP problem graphically using level curves.