Exam 4: Linear Programming Applications in Marketing, Finance, and Operations Management

A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD $\ge$ 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?

For the multiperiod production scheduling problem in the textbook, period n -1's ending inventory variable was also used as period n's beginning inventory variable.

Portfolio selection problems should acknowledge both risk and return.

Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then

It is improper to combine manufacturing costs and overtime costs in the same objective function.

Larkin Industries manufactures several lines of decorative and functional metal items. The most recent order has been for 1200 door lock units for an apartment complex developer. The sales and production departments must work together to determine delivery schedules. Each lock unit consists of three components: the knob and face plate, the actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there are three areas where the production manager is concerned about the availability of resources. These three areas, their usage by the three components, and their availability are detailed in the table. A quick look at the amounts available confirms that Larkin does not have the resources to fill this contract. A subcontractor, who can make an unlimited number of each of the three components, quotes the prices below. Develop a linear programming model that would tell Larkin how to fill the order for 1200 lock sets at the minimum cost.

Media selection problems usually determine

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper ads. Information about each medium is shown below. If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $10000, develop the model that will maximize the number reached and achieve an exposure quality if at least 1000.

A decision maker would be wise to not deviate from the optimal solution found by an LP model because it is the best solution.

Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.

Modern revenue management systems maximize revenue potential for an organization by helping to manage

To properly interpret dual prices, one must know how costs were allocated in the objective function.

The dual price for a constraint that compares funds used with funds available is .058. This means that

Revenue management methodology was originally developed for the banking industry.

Island Water Sports is a business that provides rental equipment and instruction for a variety of water sports in a resort town. On one particular morning, a decision must be made of how many Wildlife Raft Trips and how many Group Sailing Lessons should be scheduled. Each Wildlife Raft Trip requires one captain and one crew person, and can accommodate six passengers. The revenue per raft trip is $120. Ten rafts are available, and at least 30 people are on the list for reservations this morning. Each Group Sailing Lesson requires one captain and two crew people for instruction. Two boats are needed for each group. Four students form each group. There are 12 sailboats available, and at least 20 people are on the list for sailing instruction this morning. The revenue per group sailing lesson is $160. The company has 12 captains and 18 crew available this morning. The company would like to maximize the number of customers served while generating at least $1800 in revenue and honoring all reservations.

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. Current schedules yield the following information. The company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles so has gathered purchase information for each component. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.

The Tots Toys Company is trying to schedule production of two very popular toys for the next three months: a rocking horse and a scooter. Information about both toys is given below. Develop a model that would tell the company how many of each toy to produce during each month. You are to minimize total cost. Inventory cost will be levied on any items in inventory on June 30, July 31, or August 31 after demand for the month has been satisfied. Your model should make use of the relationship Beginning Inventory + Production - Demand = Ending Inventory for each month. The company wants to end the summer with 150 rocking horses and 60 scooters as beginning inventory for Sept. 1. Don't forget to define your decision variables.

Production constraints frequently take the form: beginning inventory + sales - production = ending inventory

National Wing Company (NWC) is gearing up for the new B-48 contract. Currently NWC has 100 equally qualified workers. Over the next three months NWC has made the following commitments for wing production: Each worker can either be placed in production or can train new recruits. A new recruit can be trained to be an apprentice in one month. The next month, he, himself, becomes a qualified worker (after two months from the start of training). Each trainer can train two recruits. The production rate and salary per employee is estimated below. At the end of July, NWC wishes to have no recruits or apprentices but have at least 140 full-time workers. Formulate and solve a linear program for NWC to accomplish this at minimum total cost.

A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There are 100 tons of steel available daily. A constraint on daily production could be written as: 2x₁ + 3x₂ $\le$ 100.