Exam 4: Linear Programming Applications in Marketing, Finance, and Operations Management

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

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

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

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.

​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?

Comfort Plus Inc. (CPI) manufactures a standard dining chair used in restaurants. The demand forecasts for quarter 1 (January-March) and quarter 2 (April-June) are 3700 chairs and 4200 chairs, respectively. CPI has a policy of satisfying all demand in the quarter in which it occurs. ​ The chair contains an upholstered seat that can be produced by CPI or purchased from DAP, a subcontractor. DAP currently charges $12.50 per seat, but has announced a new price of $13.75 effective April 1. CPI can produce the seat at a cost of $10.25. CPI can produce up to 3800 seats per quarter. ​ Seats that are produced or purchased in quarter 1 and used to satisfy demand in quarter 2 cost CPI $1.50 each to hold in inventory, but maximum inventory cannot exceed 300 seats. ​ Formulate this problem as a linear programming problem.

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

Information on a prospective investment for Wells Financial Services is given below. 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?

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

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.​

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.

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

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. ​ 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.

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?

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.

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.

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

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.