Exam 9: LP Applications

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.

To study consumer characteristics,attitudes,and preferences,a company would engage in

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

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

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.

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?

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 a.m. 7 10 a.m. to 2 p.m. 12 2 p.m. to 6 p.m. 10 6 p.m. to 10 p.m. 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?

​The marketing research model presented in the textbook involves minimizing total interview cost subject to interview quota guidelines.

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

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.

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.

Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.

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 Production 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 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.

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,

Media selection problems can maximize exposure quality and use number of customers reached as a constraint,or maximize the number of customers reached and use exposure quality as a constraint.

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,

Media selection problems usually determine

Revenue management methodology was originally developed for the banking industry.

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?