BA250 MANAGEMENT SCIENCE EXAMPLE PROBLEMS

CHAPTER 3#19,25,33

19)The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The Bradleys have a budget of $52,500 for next year. The government limits the number of acres of tobacco that can be planted to 100. The profit from each acre of corn is $300; the profit from each acre of tobacco is $520. Formulate a linear programming model for this problem.

a) How many acres of farmland will not be cultivated at the optimal solution? Do the Bradleys use the entire 100-acre tobacco allotment?

b) What would the profit for corn have to be for the Bradleys to plant only corn?

c) If the Bradleys can obtain an additional 100 acres of land, will the number of acres of corn and tobacco they plan to grow change?

d) If the Bradleys decide not to cultivate a 50-acre section as part of a crop recovery program, how will it affect their crop plans?

At point D only corn is planted. In order for point D to be optimal the slope of the objective function will have to be at least as great (i.e., steep) as the slope of the constraint line, x1 + x2 = 410, which is −1. Thus, the profit for corn is computed as,

−c1/520 = −1 c1 = 520

The profit for corn must be greater than $520 for the Bradleys to plant only corn.

25)Rucklehouse Public Relations has been contracted to do a survey following an election primary in New Hampshire. The firm must assign interviewers to conduct the survey by telephone or in person. One person can conduct 80 telephone interviews or 40 personal interviews in a single day. The following criteria have been established by the firm to ensure a representative survey:

– At least 3,000 interviews must be conducted.– At least 1,000 interviews must be by telephone.– At least 800 interviews must be personal.• An interviewer conducts only one type of interview each day. The cost is $50

per day for a telephone interviewer and $70 per day for a personal interviewer. Formulate a linear programming model for this problem.

a) Determine the sensitivity ranges for the daily cost of a telephone interviewer and the number of personal interviews required.

b) Does the firm conduct any more telephone and personal interviews than are required, and if so, how many more?

c) What would be the effect on the optimal solution if the firm were required by the client to increase the number of personal interviews conducted from 800 to a total of 1,200?

33) A Dept. Store in US orders 500 pairs of jeans each month from two suppliers ( China & Brazil)

Requirements:• No more than 5% defective items• Order at least 20% from each suppliera) Formulate an LP model and solve using QMb) How would you formulate this problem, if the

problem is restated as minimize the defective items while budgeting $7000 for purchasing the jeans?

China Brazil

Cost/pair of jean $11 $16

Defective Rate 0.07 0.02