Exam 9: Linear Programming Applications in Marketing, Finance, and Operations Management

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.

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

Let M be the number of units to make and B be the number of units to buy.If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed,the objective function is

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

A company makes two products,A and B.A sells for $100 and B sells for $90.The variable production costs are $30 per unit for A and $25 for B.The company's objective could be written as: Max 190x₁  55x₂.

The production scheduling problem modeled in the textbook involves capacity constraints on all of the following types of resources except

Super City Discount Department Store is open 24 hours a day.The number of cashiers need in each four hour period of a day is listed below. Period Cashiers Needed 10 p.m. to 2 a.m. 8 2 a.m. to 6 a.m. 4 6 a.m. to 10. 7 10.. to 2.. 12 2. to 6.. 10 6.. to 10 15 If cashiers work for eight consecutive hours,how many should be scheduled to begin working in each period in order to minimize the number of cashiers needed?

Let P_ij = the production of product i in period j.To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units,

Explain how a matrix could be used to define the decision variables in a blending problem.

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

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

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

Media selection problems usually determine

Describe some common feature of multiperiod financial planning models.

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

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

Blending problems arise whenever a manager must decide how to

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

Judgment is an acceptable way of obtaining input for a linear programming model.

The SMM Company,which is manufacturing a new instant salad machine,has $280,000 to spend on advertising.The product is only to be test marketed initially in the Dallas area.The money is to be spent on an advertising blitz during one weekend (Friday,Saturday,and Sunday)in January,and SMM is limited to television advertising. The company has three options available: daytime advertising,evening news advertising and the Super Bowl.Even though the Super Bowl is a national telecast,the Dallas Cowboys will be playing in it,and hence,the viewing audience will be especially large in the Dallas area.A mixture of one-minute TV spots is desired.The table below gives pertinent data: Cost Per Ad Estimated New Audience Reached With Each Ad Daytime \ 5,000 3,000 Evening News \ 7,000 4,000 Super Bowl \ 100,000 75,000 SMM has decided to take out at least one ad in each option.Further,there are only two Super Bowl ad spots available.There are 10 daytime spots and 6 evening news spots available daily.SMM wants to have at least 5 ads per day,but spend no more than $50,000 on Friday and no more than $75,000 on Saturday.Formulate and solve a linear program to help SMM decide how the company should advertise over the weekend.