Exam 4: Linear Programming Applications in Marketing, finance, and OM

Media selection problems usually determine

Which operations management application model is most likely to have an objective function that minimizes the sum of manufacturing costs,purchasing costs,and overtime costs?

Production constraints frequently take the form: ​ Beginning inventory + Sales − Production = Ending inventory

Comfort Plus Inc.(CPI)manufactures a standard dining chair used in restaurants.The demand forecasts for quarter 1 (January-March)and quarter 2 (April-June)are 3700 chairs and 4200 chairs,respectively.CPI has a policy of satisfying all demand in the quarter in which it occurs.The chair contains an upholstered seat that can be produced by CPI or purchased from DAP,a subcontractor.DAP currently charges $12.50 per seat,but has announced a new price of $13.75,effective April 1.CPI can produce the seat at a cost of $10.25.CPI can produce up to 3800 seats per quarter.​ Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $1.50 each to hold in inventory,but maximum inventory cannot exceed 300 seats.​ Formulate this problem as a linear programming problem.

The dual price for a constraint that compares funds used with funds available is 0.058.This means that

A company produces two different products from steel.One requires 3 tons of steel and the other requires 5 tons.There are 100 tons of steel available daily.A constraint on daily production could be written as: 3x₁ + 5x₂ ≥ 100.

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.

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 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 are estimated below. ​ At the end of July,NWC wishes to have no recruits or apprentices but at least 140 full-time workers.Formulate and solve a linear program for NWC to accomplish this at minimum total cost.

Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.

A mutual fund manager must decide how much money to invest in Atlantic Oil (A)and how much to invest in Pacific Oil (P).At least 60% of the money invested in the two oil companies must be in Pacific Oil.A correct modeling of this constraint is

Island Water Sports provides rental equipment and instruction for a variety of water sports in a resort town.On one particular morning,a decision must be made on 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.

Blending problems arise whenever a manager must decide how to

To study consumer characteristics,attitudes,and preferences,a company would engage in

If a real-world problem is correctly formulated,it is NOT possible to have alternative optimal solutions.

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

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

An LP model for 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.There is a constraint that HD ≥ 100.The solution indicates that interviewing another homeowner during the day will increase costs by 10.00.What does this tell you about the HD variable? ​

If P_ij = the production of product i in period j,then to indicate that the limit on production of the company's three products in period 2 is 400,we would express it as ​

A&C Distributors represents many outdoor products companies and schedules deliveries to discount stores,garden centers,and hardware stores.Currently,scheduling needs to be done for two lawn sprinklers,the Water Wave and Spring Shower models.Requirements for shipment to a warehouse for a national chain of garden centers are shown below. Let S_ij be the number of units of sprinkler i shipped in month j,where i = 1 or 2,and j = 1,2,or 3.Let W_ij be the number of sprinklers that are at the warehouse at the end of a month,in excess of the minimum requirement.

It can take longer to collect the data for a large-scale linear programming model than it does for either the formulation of the model or the development of the computer solution.