CH 4

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

−.5A + .5B − .5C ≤ 0

Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If Ai measures the labor hours allocated to department i and Tij the hours transferred from department i to department j, then

A3 − T13 − T23 + T32 + T34 = 2500

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

Min 2M + 3B

(T/F) An LP model for a large-scale production scheduling problem involving numerous products, machines, and time periods can require thousands of decision variables and constraints.

T

(T/F) For the marketing research problem presented in the textbook, the research firm's objective is to conduct the market survey so as to meet the client's needs at a minimum cost.

T

(T/F) 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.

T

(T/F) Portfolio selection problems should acknowledge both risk and return.

T

Media selection problems usually determine

how many times to use each media source.

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

if more funds can be obtained at a rate of 5.5%, some should be.

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

marketing research.

For a portfolio selection problem with the objective of maximizing expected return, the dual price for the available funds constraint provides information about the

return from additional investment funds

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?

the dual price for the HD constraint is −10.

(T/F) A constraint with non-zero slack will have a positive dual price, and a constraint with non-zero surplus will have a negative dual price.

F

(T/F) If a real-world problem is correctly formulated, it is not possible to have alternative optimal solutions.

F

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

F

(T/F) It is improper to combine manufacturing costs and overtime costs in the same objective function.

F

(T/F) Production constraints frequently take the form: beginning inventory + sales − production = ending inventory

F

If Pij = 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,

P12 + P22 + P32 ≤ 400

Let Pij = 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,

P13 − P14 ≤ 100; P14 − P13 ≤ 100

(T/F) To properly interpret dual prices, one must know how costs were allocated in the objective function.

T

The objective function for portfolio selection problems usually is maximization of expected return or

minimization of risk