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

An LP model for a large-scale production scheduling problem involving numerous products, machines, and time periods can require thousands of decision variables and constraints.

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

Evans Enterprises has bought a prime parcel of beachfront property and plans to build a luxury hotel. After meeting with the architectural team, the Evans family has drawn up some information to make preliminary plans for construction. Excluding the suites, which are not part of this decision, the hotel will have four kinds of rooms: beachfront non-smoking, beachfront smoking, lagoon view non-smoking, and lagoon view smoking. In order to decide how many of each of the four kinds of rooms to plan for, the Evans family will consider the following information. a.After adjusting for expected occupancy, the average nightly revenue for a beachfront non-smoking room is $175.The average nightly revenue for a lagoon view non-smoking room is $130.Smokers will be charged an extra $15. b.Construction costs vary.The cost estimate for a lagoon view room is $12,000 and for a beachfront room is $15,000.Air purifying systems and additional smoke detectors and sprinklers ad $3000 to the cost of any smoking room.Evans Enterprises has raised $6.3 million in construction guarantees for this portion of the building. c.There will be at least 100 but no more than 180 beachfront rooms. d.Design considerations require that the number of lagoon view rooms be at least 1.5 times the number of beachfront rooms, and no more than 2.5 times that number. e.Industry trends recommend that the number of smoking rooms be no more than 50% of the number of non-smoking rooms.Develop the linear programming model to maximize revenue.

Describe some common feature of multiperiod financial planning models.

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

A&C Distributors is a company that 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. Month Shipping Capacity Product Minimum Requirement Unit Cost to Ship Per Unit Inventory Cost March 8000 Water Wave 3000 .30 .06 Spring Shower 1800 .25 .05 April 7000 Water Wave Spring Shower 4000 4000 .40 .30 .09 .06 May 6000 Water Wave 5000 .50 .12 Spring shower 2000 .35 .07 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. a.Write the portion of the objective function that minimizes shipping costs. b.An inventory cost is assessed against this ending inventory.Give the portion of the objective function that represents inventory cost. c.There will be three constraints that guarantee, for each month, that the total number of sprinklers shipped will not exceed the shipping capacity.Write these three constraints. d.There are six constraints that work with inventory and the number of units shipped, making sure that enough sprinklers are shipped to meet the minimum requirements.Write these six constraints.

Media selection problems usually determine

The Meredith Ribbon Company produces paper and fabric decorative ribbon which it sells to paper products companies and craft stores. The demand for ribbon is seasonal. Information about projected demand and production for a particular type of ribbon is given. Demand (yards) Froduction Cost Per Yard Froduction Capacity (yards) Quarter 1 10,000 .03 30,000 Quarter 2 18,000 .04 20,000 Quarter 3 16,000 .06 20,000 Quarter 4 30,000 .08 15,000 An inventory holding cost of $.005 is levied on every yard of ribbon carried over from one quarter to the next. a.Define the decision variables needed to model this problem. b.The objective is to minimize total cost, the sum of production and inventory holding cost.Give the objection function. c.Write the production capacity constraints. d.Write the constraints that balance inventory, production, and demand for each quarter.Assume there is no beginning inventory in quarter 1. e.To attempt to balance the production and avoid large changes in the workforce, production in period 1 must be within 5000 yards of production in period 2.Write this constraint.

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. Component Requirements Plastic Time Space Cost to Manufacture Cost to Purchase Front 3 10 2 8 12 Seat/Frame 4 6 2 6 9 Rear wheel (each) .5 2 1 1 3 Available 50000 160000 30000 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.

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

For a portfolio selection problem with the objective of maximizing expected return, the dual price for the available funds constraint provides information about the

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,

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

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?

A constraint with non-zero slack will have a positive dual price, and a constraint with non-zero surplus will have a negative dual price.

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

Media selection problems can maximize exposure quality and use number of customers reached as a constraint, or maximize the number of customers reached and use exposure quality as a constraint.

What benefits exist in using linear programming for production scheduling problems?