Exam 9: LP Applications

G and P Manufacturing would like to minimize the labor cost of producing dishwasher motors for a major appliance manufacturer.Although two models of motors exist,the finished models are indistinguishable from one another;their cost difference is due to a different production sequence.The time in hours required for each model in each production area is tabled here,along with the labor cost. ​ Model 1 Model 2 Area A 15 3 Area B 4 10 Area C 4 8 Cost 80 65 Currently labor assignments provide for 10,000 hours in each of Areas A and B and 18000 hours in Area C.If 2000 hours are available to be transferred from area B to Area A,3000 hours are available to be transferred from area C to either Areas A or B,develop the linear programming model whose solution would tell G&P how many of each model to produce and how to allocate the workforce.

Portfolio selection problems should acknowledge both risk and return.

​Describe three situations where variations of the workforce assignment model could be applied.

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

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

​Interpret the dual price for any two of the following constraints: 1)the available funds in a portfolio selection model, 2)the cash requirement due at the beginning of a year in a financial planning model,and 3)the manufacturing capacity in a make-or-buy decision model.

A marketing research firm must determine how many daytime interviews (D)and evening interviews (E)to conduct.At least 40% of the interviews must be in the evening.A correct modeling of this constraint is: -0.4D + 0.6E > 0.​

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

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. 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 porti on of the objective function that represents inventory cost. There will be three constraints that guarantee, for each month, that the total number of c. sprinklers shipped will not exceed the shipping capacity. Write these three constraints. There are six constraints that work with inventory and the number of units shipped, making d. sure that enough sprinklers are shipped to meet the minimum requirements. Write these six constr aints.

FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture,a nut mixture,and a cereal mixture.Information about the three ingredients (per ounce)is shown below. ​ Ingredient Cost Volume Fat Grams Calories Dried Fruit .35 1/4 cup 0 150 Nut Mix .50 3/8 cup 10 400 Cereal Mix .20 1 cup 1 50 The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the TrailTime blend.TrailTime is packaged in boxes that will hold between three and four cups.The blend should contain no more than 1000 calories and no more than 25 grams of fat.Dried fruit must be at least 20% of the volume of the mixture,and nuts must be no more than 15% of the weight of the mixture.Develop a model that meets these restrictions and minimizes the cost of the blend.

​Discuss at least three additional considerations that might be included in media selection LP models more complex than the one covered in the text.

​Which of the operations management applications modeled in the text has an objective function that minimizes the sum of manufacturing costs,purchasing costs,and overtime costs?

A mutual fund manager is deciding how much money to invest in each of three companies: Atlantic Oil (A),Pacific Oil (P),and Gulf Oil (G).The money invested in Gulf Oil must equal at least 30% of the money invested in the other two companies.A correct modeling of this constraint is​

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

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

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.

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

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

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. Plastic Time Monthly Demand Monthly Demand Summer Schedule Available Available Horse Scooter June 3500 2100 220 450 July 5000 3000 350 700 August 4800 2500 600 520

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