Exam 9: LP Applications

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.

If an LP problem is not correctly formulated,the computer software will indicate it is infeasible when trying to solve it.

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

​Blending problems arise whenever a manager must decide how to

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.

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.

​In a production scheduling LP,the demand requirement constraint for a time period takes the form

​Describe some common feature of multiperiod financial planning models.

​Data collection for large-scale LP models can be more time-consuming than either the formulation of the model or the development of the computer solution.

Department 3 has 2500 hours.Transfers are allowed to departments 2 and 4,and from departments 1 and 2.If A_i measures the labor hours allocated to department i and T_ij the hours transferred from department i to department j,then

​Why should decision makers who are primarily concerned with marketing or finance or production know about linear programming?

Compared to the problems in the textbook,real-world problems generally require more variables and constraints.

​Discuss several resource allocation problems that can be modeled by varying the workforce assignment model.

​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

BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year.The advertising budget is $10,000,000.Because BP wants to push its new sodas,at least one-half of the advertising budget is to be devoted to new soda advertising.However,at least $2,000,000 is to be spent on its traditional sodas.BP estimates that each dollar spent on traditional sodas will translate into 100 cans sold,whereas,because of the harder sell needed for new products,each dollar spent on new sodas will translate into 50 cans sold. To attract new customers BP has lowered its profit margin on new sodas to 2 cents per can as compared to 4 cents per can for traditional sodas.How should BP allocate its advertising budget if it wants to maximize its profits while selling at least 750 million cans?

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

The media selection model presented in the textbook involves maximizing the number of potential customers reached subject to a minimum total exposure quality rating.

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. ​ Resource Knob and Plate Lock Key (each) Available Brass Alloy 12 5 1 15000 units Machining 18 20 10 36000 minutes Finishing 15 5 1 12000 minutes 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. ​ Component Subcontractor Cost Larkin Cost Knob and Plate 10.00 6.00 Lock 9.00 4.00 Keys (set of 2) 1.00 .50 Develop a linear programming model that would tell Larkin how to fill the order for 1200 lock sets at the minimum cost.

​Discuss the need for the use of judgment or other subjective methods in mathematical modeling.

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 ≤ 100.