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

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

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

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.

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

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.

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.

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

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

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.

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,

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.

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.

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

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

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?

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,