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Situational Cases on Integer Programming Problem

Case-I

The Otter Creek Winery produces three kinds of table wine – a blush, a

white and a red. The winery has 30,000 pounds of grapes available to

produce wine this season. A cask of blush requires 360 pounds of

grapes, a cask of white requires 375 pounds, and a cask of red requires

410 pounds. The winery has enough storage space in its aging room to

store 67 casks of wine. The winery has 2,200 hours of production

capacity, and it requires 14 hours to produce a cask of blush, 10 hours to

produce a cask of white, and 18 hours to produce a cask of red. From

records of previous years’ sales, the winery knows it will sell at least

twice as much blush as red and at least 1.5 times as much white as blush.

The profit for a cask of blush is $12,100, the profit for a cask of white is

$8,700, and the profit for a cask of red is $10,500. The winery wants to

know the number of casks of each table wine to produce. Formulate and

solve an integer programming model for this problem.

Case –II

Corsouth Mortgage Associates is a large home mortgage firm in the

Southeast. It has a pool of permanent and temporary computer operators

who process mortgage accounts, including posting payments and

updating escrow accounts for insurance and taxes. A permanent operator

can process 220 accounts per day, and a temporary operator can process

140 accounts per day. On average, the firm must process and update at

least 6,300 accounts daily. The company has 32 computer workstations

available. Permanent and temporary operators work 8 hours per day. A

permanent operator averages about 0.4 errors per day, whereas a

temporary operator averages 0.9 errors per day. The company wants to

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limit errors to 15 per day. A permanent operator is paid $120 per day,

whereas a temporary operator is paid $75 per day. Corsouth wants to

determine the number of permanent and temporary operators it need to

minimize cost. Formulate and solve an integer programming model for

this problem and compare this solution to the non- integer solution.

In the above problem, Corsouth Mortgage Associates is considering

hiring some hourly, part-time computer operators in addition to its

permanent and temporary operators. A part- time operator can process

12 accounts per hour, averages 0.16 errors per hour, and is paid $4.50

per hour. Corsouth wants to know the number of permanent and

temporary employees it should use, plus the number of part-time hours it

should arrange for. Formulate and solve a mixed integer model for this

problem.