Exam 9: Linear Programming Applications

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

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

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

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

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: 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.

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.

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.

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. 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,

Winslow Savings has $20 million available for investment.It wishes to invest over the next four months in such a way that it will maximize the total interest earned over the four month period as well as have at least $10 million available at the start of the fifth month for a high rise building venture in which it will be participating. For the time being,Winslow wishes to invest only in 2-month government bonds (earning 2% over the 2-month period)and 3-month construction loans (earning 6% over the 3-month period).Each of these is available each month for investment.Funds not invested in these two investments are liquid and earn 3/4 of 1% per month when invested locally. Formulate and solve a linear program that will help Winslow Savings determine how to invest over the next four months if at no time does it wish to have more than $8 million in either government bonds or construction loans.

Portfolio selection problems should acknowledge both risk and return.

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.

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 > 100.The solution indicates that interviewing another homeowner during the day will increase costs by 10.00.What do you know?

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

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

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.

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

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. 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.

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

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.