## DISCUSSION QUESTIONS AND PROBLEMS 259

DISCUSSION QUESTIONS AND PROBLEMS 259

Table for Problem 6-26

CHARLOTTE TULSA MEMPHIS BUFFALO

Monthly capacity (units) 7,000 6,500 7,250 7500

Monthly fixed cost (S) $30000 $35000 334.000 332.000

Shipping to Region I (Slunit) $ 5 $ 8 $ 3 $ 2

Shipping to Region 2 (S/unit) $ 4 $ 5 $ 3 $ 9

Shipping to Region 3 (S/unit) $ 5 $ 3 S 4 $ 10

REGION 1 REGION 2 REGION 3

Monthly demand (units) 3.000 4.000 6.50)

Table for Problem 6-27 Table for Problem 6-29

A B C D E F G H FIXED VARIABLE SELLING

DEMAND COST COST PRICE

I 25 5 55 5 35 IS 65 45

Book 4 6.000 $10000 $20 $34

(a) Which two locations will minimize the total W

mileage from the trauma centers to the high-

need areas? Which locations should be desig- For each book. the maximum demand. fixed

natcd to receive injured persons from each of the cost of publishing. variable COSt. and selling price

high-need locations? are provided. Rollins has the capacity to pub-

(b) Now solve this as a set covering model, assum- lish a total of 20,000 books. Which books should

ing that the hospital wants to keep the distance be selected. and how many of each should be

between a high-need location and a trauma cen- published?

ter to no more than 35 miles. 6-30 Sandy Edge is president of Edge File Works. a

6-28 The Columbia Furniture Mart manufactures desks, firm that manufactures two types of metal file

tables. and chairs. In order to manufacture these cabinets. The demand for the two-drawer model

products, Columbia must rent the appropriate equip- is 650 cabinets per week; demand for the three-

ment at a weekly cost of $2,000 for desks, $2.500 drawer cabinet is 400 per week. Edge has a weekly

for tables. and $1.500 for chairs. The labor and ma- operating capacity of 1.600 hours. with the two-

terial requirements for each product are shown in drawer cabinet taking 1.5 hours to produce and

the following table. along with the selling price and the three-drawer cabinet requiring 2 hours. Each

variable cost to manufacture. two-drawer model sold yields a $12 profit. and

the profit for the three-drawer model is $I4. Edge

has listed the following goals. in rank order:

LABOR LUMBER SALES VARIABLE

HOURS (so. rr.) PRICE COST Rank 1: Attain a profit as close to SI 2,000 as pos-

1 sible each week.

Desks 4 ‘2 $135 39; Rank 2: Avoid underutilization of the firm’s pro

Chairs 2 6 5 50 533 Rank 3: Sell as many two- and three-drawer cabi-

nets as the demand indicates.

There are 2.500 labor hours and 8.000 square Set up and solve this problem as a goal program-

feet of lumber available each week. Determine the ming model.

PTOdUCt mix that maximizes weekly profit. 6-31 Eric Weiss. marketing director for Charter Power

6-29 Rollins Publishing needs to decide what textbooks and Light. is about to begin an advertising campaign

from the table at the top of the next column to publish. promoting energy conservation. Each TV ad costs

DISCUSSION QUESTIONS AND PROBLEMS 257

be invested. (2) the money is to be spread among at If selected, an item must be shipped in its en-

least five investments. (3) no more than one type of tirety {i.e., partial shipments are not allowed). Of

bond can be purchased. (4) at least two utility stocks items B. C. and D. at least two items must be se-

must be purchased, and (5) at least two regular lected. If item B is selected. then item G cannot be

stocks must be purchased. Formulate this as a 0-1 selected. Which items should be selected to maxi-

IP problem for Ms. Drexler to maximize expected mize the value of the shipment?

return. 501W? ll by using Excel. 6-21 The Greenville Ride have $19 million available to

6-19 Porter Investments needs to develop an investment sign free agent pitchers for the next season. The fol-

portfolio for Mrs. Singh from the following list of lowing table provides the relevant information for

possible investments: eight pitchers who are available for signing. such as

whether each throws right or left handed. whether

INVESTMENT COST EXPECTED RETURN each is a starter or reliever. the cost in millions of

dollars to sign each, and the relative value of each on

A $ 10’000 $ 700 the market on a scale of l to 10 (10 = highest).

B $ 12.000 $ 1.000

C $ 3.500 $ 391) START] COST

o 5 5.000 s 500 PITCHER THROWS RELIEF (MILLIONS) VALUE

E S 8.500 $ 751) A L R $9 3

F $ 8.000 $ 641) B R S $4 5

G $ 4,000 $ 300 C R S $5 6

Mrs. Singh has a total of $60,000 to invest. The D L S $5 5

following conditions must be met: (1) lf investment b R R $6 8

F is chosen, then investment G must also be part of F R R $3 5

the portfolio, (2) at least four investments should be G L s $8 7

chosen, and (3) of investment A and R, exactly one H R S $2 4

must be included. What stocks should be included in

Mrs. Singh’s portfolio? The Ride feel the following needs exist for next

6-20 A truck with the capacity to load 2,200 cubic feet 8833″”: (I) at least two right-handed pitchers, (2) at

of cargo is available to transport items selected from least

DISCUSSION QUESTIONS AND PROBLEMS 261

-EXPECTED 6-37 Consider the following NLP problem:

INVESTMENT DESCRIPTION RETURN Maximize IOX, + 15×2 + 25×3

A IRA (felifcmcml 35% subject to the constraints

B llilretlilployer’s retirement 4.5% XI + X3 + X3 .5 I 2

C Del‘erredincome 8.0% X? + XE S 32

(retirement) ZXI + X; _<_ 44

D Unity mutual fund 7.0% X..X2. X3 2 0

E L’bmy “mum! fund 75% (a) Set up and solve the model by using Solver.

F Mme)’ market 55% Use a starting value of zero for each decision

variable.

Theo’s investment goals are as follows and can be (b) ls the solution obtained a local optimal or global

ranked according lo the weights shown in parenthesis. optimal solution? How do you know?

WhICh. Investments should be Included. In Theo s 6-38 Consider the following NLP problem:

portfolio. and how much should he Invest In each?

Goal I: (25.) Invest all funds available. Maximi7e