Mat 540 week 8 new 2015 data


MAT540

Week 8 Homework

Chapter 4

1. Grafton Metalworks Guild sums metal disparagements from six unanalogous ores it mines. The guild has an adjust from a customer to sum an disparagement that contains indelicate metals according to the aftercited localations: at insignificantest 21% of metal A, no aggravate than 12% of metal B, no aggravate than 7% of metal C and betwixt 30% and 65% of metal D. The uniformity of the indelicate metals in each of the six ores and the raze of impurities in each ore are granted in the aftercited 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 guild wants to distinguish the sum of each ore to use per ton of the disparagement that succeed minimize the consume per ton of the disparagement.

a. Formulate a straight programming design for this gist.

b. Work-out the design by using the computer.

2. As a outcome of a recently passed reckoning, a congressman’s environs has been tabulated $4 darling for programs and contrivances. It is up to the congressman to career how to portio the capital. The congressman has careerd to tabulate the capital to indelicate ongoing programs consequently of their avail to his environs – a job trailing program, a parks contrivance, a sanitation contrivance, and a fickle library. However, the congressman wants to portio the capital in a sort that succeed satisfied the most voters, or, in other tone, movables him the most votes in the upcoming acceptance. His staff’s estimates of the calculate of votes movablesed per dollar gone-by for the diversified programs are as follows.

Program

Votes/ Dollar

Job trailing

0.02

Parks

0.09

Sanitation

0.06

Mobile library

0.04

In adjust as-well to suffice diversified national potent citizens who financed his acceptance, he is obligated to behold the aftercited guidelines:

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Week 8

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 None of the programs can take aggravate than 40% of the whole allocation.

 The sum tabulated to parks cannot excel the whole tabulated to twain the sanitation contrivance and the fickle library

 The sum tabulated to job trailing must at insignificantest similar the sum gone-by on the sanitation contrivance.

Any capital not gone-by in the environs succeed be returned to the government; hence, the congressman wants to consume it all. The congressman wants to distinguish the sum to tabulate to each program to maximize his votes.

a. Formulate a straight programming design for this gist.

b. Work-out the design by using the computer.

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

 Betwixt 1,500 and 2,000 calories

 At insignificantest 5 mg of iron

 At insignificantest 20 but no aggravate than 60 g of fat

 At insignificantest 30 g of protein

 At insignificantest 40 g of carbohydrates

 No aggravate than 30 mg of cholesterol

She fines the menu from seven basic foundation items, as follows, delay the nutritional contributions per pulverize and the consume 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 fine a menu to as the nutritional guidelines period minimizing the whole consume per serving.

a. Formulate a straight programming design for this gist.

MAT540 Homework

Week 8

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b. Work-out the design by using the computer

c. If a serving of each of the foundation items (other than agree) was scant to no aggravate than a half pulverize, what movables would this possess on the discerption?

4. The Cabin Creek Coal (CCC) Guild operates three mines in Kentucky and West Virginia, and it arrangement coal to indelicate profit government settles along the East Coast. The consume of shipping coal from each mine to each settle, the calibre at each of the three mines and the ask-for at each settle are shown in the aftercited table:

Plant

Mine

1

2

3

4

Mine Calibre (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 consume 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 satisfied per ton of coal at each mine is as follows:

Mine

% Ash

% Sulfur

1

9

6

2

5

4

3

4

3

Each settle has unanalogous cleaning equipment. Settle 1 requires that the coal it takes possess no aggravate than 6% ash and 5% sulfur; settle 2 coal can possess no aggravate than 5% ash and sulfur in-one; settle 3 can possess no aggravate than 5% ash and 7% sulfur; and settle 4 can possess no aggravate than 6% ash and sulfur in-one. CCC wabts to particularize the sum of coal to sum at each mine and ship to its customers that succeed minimize its whole consume.

a. Formulate a straight programming design for this gist.

b. Work-out this design by using the computer.

5. Joe Henderson runs a insignificant metal compressiveness treasure. The treasure contains three meanss – a teach constrain, a lathe, and a grinder. Joe has three operators, each certified to composition on all three meanss. However, each operator completes improve on some meanss than on others. The treasure has

MAT540 Homework

Week 8

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

Operator

Drill Constrain (min)

Lathe (min)

Grinder (min)

1

23

18

35

2

41

30

28

3

25

36

18

Joe Henderson wants to attribute one operator to each means so that the topal gratuitous season for all three operators is minimized.

a. Formulate a straight programming design for this gist.

b. Work-out the design by using the computer

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

6. The Cash and Carry Building Supply Guild has taked the aftercited adjust for tables in three lengths:

Length

Order (quantity)

7 ft.

700

9 ft.

1,200

10 ft.

300

The guild has 25-foot standard-length tables in fund. Therefore, the standard-length tables must be cut into the lengths essential to as adjust requirements. Naturally, the guild wishes to minimize the calculate of standard-length tables used.

a. Formulate a straight programming design for this gist.

b. Work-out the design by using the computer

c. When a table is cut in a local archetype, the sum of table left aggravate is referred to as “trim-loss.” Reformulate the straight programming design for this gist, lofty that the external is to minimize deck privation rather than to minimize the whole calculate of tables used, and work-out the design. How does this pretend the discerption?