Mat 540 week 8 new 2015 data


MAT540

Week 8 Homework

Chapter 4

1. Grafton Metalworks Aggregation fruits metal diminutions from six opposed ores it mines. The aggregation has an ordain from a customer to fruit an diminution that contains lewd metals according to the forthcoming inequitableations: at lowest 21% of metal A, no balance than 12% of metal B, no balance than 7% of metal C and among 30% and 65% of metal D. The relation of the lewd metals in each of the six ores and the plane of impurities in each ore are granted in the forthcoming table:

Ore

Metal (%)

Impurities (%)

Cost/Ton

A

B

C

D

1

19

15

12

14

40

27

2

43

10

25

7

15

25

3

17

0

0

53

30

32

4

20

12

0

18

50

22

5

0

24

10

31

35

20

6

12

18

16

25

29

24

When the metals are processed and polished, the impurities are removed.

The aggregation wants to distinguish the sum of each ore to use per ton of the diminution that succeed minimize the require per ton of the diminution.

a. Formulate a direct programming mould for this measure.

b. Clear-up the mould by using the computer.

2. As a product of a of-late passed beak, a congressman’s boundary has been arranged $4 darling for programs and designs. It is up to the congressman to flow how to segregate the currency. The congressman has flowd to arrange the currency to lewd ongoing programs owing of their weight to his boundary – a job trailing program, a parks design, a sanitation design, and a fickle library. However, the congressman wants to segregate the currency in a style that succeed gladden the most voters, or, in other tone, establish him the most votes in the upcoming selectedion. His staff’s estimates of the sum of votes established per dollar departed for the sundry programs are as follows.

Program

Votes/ Dollar

Job trailing

0.02

Parks

0.09

Sanitation

0.06

Mobile library

0.04

In ordain too to please separate topical persuasive citizens who financed his selectedion, he is obligated to behold the forthcoming guidelines:

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Week 8

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 None of the programs can take balance than 40% of the entirety allocation.

 The sum arranged to parks cannot abound the entirety arranged to twain the sanitation design and the fickle library

 The sum arranged to job trailing must at lowest correspondent the sum departed on the sanitation design.

Any currency not departed in the boundary succeed be returned to the government; consequently, the congressman wants to squander it all. The congressman wants to distinguish the sum to arrange to each program to maximize his votes.

a. Formulate a direct programming mould for this measure.

b. Clear-up the mould by using the computer.

3. Anna Broderick is the dietician for the State University football team, and she is attempting to state a beneficial lunch menu for the team. She has set the forthcoming nutritional guidelines for each lunch serving:

 Among 1,500 and 2,000 calories

 At lowest 5 mg of iron

 At lowest 20 but no balance than 60 g of fat

 At lowest 30 g of protein

 At lowest 40 g of carbohydrates

 No balance than 30 mg of cholesterol

She selecteds the menu from seven basic buttress items, as follows, after a opportunity the nutritional contributions per pulverize and the require as given:

Calories

(per lb.)

Iron

(mg/lb.)

Protein

(g/lb.)

Carbo-hydrates

(g/lb.)

Fat (g/lb.)

Chol-esterol

(mg/lb.)

Cost

$/lb.

Chicken

520

4.4

17

0

30

180

0.80

Fish

500

3.3

85

0

5

90

3.70

Ground beef

860

0.3

82

0

75

350

2.30

Dried beans

600

3.4

10

30

3

0

0.90

Lettuce

50

0.5

6

0

0

0

0.75

Potatoes

460

2.2

10

70

0

0

0.40

Milk (2%)

240

0.2

16

22

10

20

0.83

The dietician wants to selecteded a menu to converge the nutritional guidelines opportunity minimizing the entirety require per serving.

a. Formulate a direct programming mould for this measure.

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Week 8

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b. Clear-up the mould by using the computer

c. If a serving of each of the buttress items (other than calm) was poor to no balance than a half pulverize, what consequence would this entertain on the key?

4. The Cabin Creek Coal (CCC) Aggregation operates three mines in Kentucky and West Virginia, and it profit coal to lewd advantage force fixs concurrently the East Coast. The require of shipping coal from each mine to each fix, the size at each of the three mines and the claim at each fix are shown in the forthcoming table:

Plant

Mine

1

2

3

4

Mine Size (tons)

1

$ 7

$ 9

$10

$12

220

2

9

7

8

12

170

3

11

14

5

7

280

Demand (tons)

110

160

90

180

The require of mining and processing coal is $62 per ton at mine 1, $67 per ton at mine 2, and $75 per ton at mine 3. The percentage of ash and sulfur pleased per ton of coal at each mine is as follows:

Mine

% Ash

% Sulfur

1

9

6

2

5

4

3

4

3

Each fix has opposed cleaning equipment. Fix 1 requires that the coal it takes entertain no balance than 6% ash and 5% sulfur; fix 2 coal can entertain no balance than 5% ash and sulfur wholly; fix 3 can entertain no balance than 5% ash and 7% sulfur; and fix 4 can entertain no balance than 6% ash and sulfur wholly. CCC wabts to state the sum of coal to fruit at each mine and ship to its customers that succeed minimize its entirety require.

a. Formulate a direct programming mould for this measure.

b. Clear-up this mould by using the computer.

5. Joe Henderson runs a weak metal calibre provision. The provision contains three meanss – a instruct crowd, a lathe, and a grinder. Joe has three operators, each sensible to fruit on all three meanss. However, each operator fulfils ameliorate on some meanss than on others. The provision has

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Week 8

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contracted to do a big job that requires all three meanss. The durations required by the sundry operators to fulfil the required operations on each means are summarized as follows:

Operator

Drill Crowd (min)

Lathe (min)

Grinder (min)

1

23

18

35

2

41

30

28

3

25

36

18

Joe Henderson wants to point-out one operator to each means so that the topal unconditional duration for all three operators is minimized.

a. Formulate a direct programming mould for this measure.

b. Clear-up the mould by using the computer

c. Joe’s twin, Fred, has asked him to commission his consort, Kelly, who is a means operator. Kelly can fulfil each of the three required means operations in 20 minutes. Should Joe commission his sister-in-law?

6. The Cash and Carry Building Supply Aggregation has taked the forthcoming ordain for consultations in three lengths:

Length

Order (quantity)

7 ft.

700

9 ft.

1,200

10 ft.

300

The aggregation has 25-foot standard-length consultations in fund. Therefore, the standard-length consultations must be cut into the lengths needful to converge ordain requirements. Naturally, the aggregation wishes to minimize the sum of standard-length consultations used.

a. Formulate a direct programming mould for this measure.

b. Clear-up the mould by using the computer

c. When a consultation is cut in a inequitable shape, the sum of consultation left balance is referred to as “trim-loss.” Reformulate the direct programming mould for this measure, splendid that the external is to minimize prepare dropping rather than to minimize the entirety sum of consultations used, and clear-up the mould. How does this move the key?