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

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.

Information on a prospective investment for Wells Financial Services is given below. Period 1 2 3 4 Loan Funds Available 3000 7000 4000 5000 Investment Income (\% of previous period's investment) 110\% 112\% 113\% Maximum Investment 4500 8000 6000 7500 Payroll Payment 100 120 150 100 In each period,funds available for investment come from two sources: loan funds and income from the previous period's investment.Expenses,or cash outflows,in each period must include repayment of the previous period's loan plus 8.5% interest,and the current payroll payment.In addition,to end the planning horizon,investment income from period 4 (at 110% of the investment)must be sufficient to cover the loan plus interest from period 4.The difference in these two quantities represents net income,and is to be maximized.How much should be borrowed and how much should be invested each period?

Portfolio selection problems should acknowledge both risk and return.

Wes Wheeler is the production manager of Wheeler Wheels,Inc.Wes has just received orders for 1,000 standard wheels and 1,250 deluxe wheels next month and for 800 standard and 1,500 deluxe wheels the following month.All orders are to be filled. The cost of producing standard wheels is $10 and deluxe wheels is $16.Overtime rates are 50% higher.There are 1,000 hours of regular time and 500 hours of overtime available each month.It takes .5 hour to make a standard wheel and .6 hour to make a deluxe wheel.The cost of storing one wheel from one month to the next is $2. Wes wants to develop a two-month production schedule for standard and deluxe wheels.Formulate this production planning problem as a linear program.

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

Target Shirt Company makes three varieties of shirts: Collegiate,Traditional and European.These shirts are made from different combinations of cotton and polyester. The cost per yard of unblended cotton is $5 and for unblended polyester is $4.Target can receive up to 4,000 yards of raw cotton and 3,000 yards of raw polyester fabric weekly.The table below pertinent data concerning the manufacture of the shirts. Coll egiate Traditional European Total Yards 1.00 1.20 .90 Fabric At least 50 \% cotton No more than 20 \% polyester As much as 80 \% polyester Weekly 500 650 280 Weekly 600 850 675 Selling \1 4.00 \ 15.00 \ 18.00 Formulate and solve this blending problem as a linear program.

The primary limitation of linear programming's applicability is the requirement that all decision variables be nonnegative.

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?

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,

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.

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 0 150 Nut Mix .50 3/8 10 400 Cereal Mix .20 1 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.

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.

National Wing Company (NWC)is gearing up for the new B-48 contract.Currently NWC has 100 equally qualified workers.Over the next three months NWC has made the following commitments for wing production: Month Wing Froduction May 20 June 24 July 30 Each worker can either be placed in production or can train new recruits.A new recruit can be trained to be an apprentice in one month.The next month,he,himself,becomes a qualified worker (after two months from the start of training).Each trainer can train two recruits.The production rate and salary per employee is estimated below. Employee Froduction Rate (Wings/Month) Salary Per Month Production .6 \ 3,000 Trainer .3 3,300 Apprentice .4 2,600 Recruit .05 2,200 At the end of July,NWC wishes to have no recruits or apprentices but have at least 140 full-time workers.Formulate and solve a linear program for NWC to accomplish this at minimum total cost.

A decision maker would be wise to not deviate from the optimal solution found by an LP model because it is the best solution.

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

Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.

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

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.

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

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