group asgmt no 2 ee

Semester I 2012/2013 Kohort 1

BWM 21403 – MATEMATIK IVGROUP 1 EE ASSIGNMENT NO.2

Q1 Find the root of that lies in the interval [1, 1.5] by using Bisection

method. Iterate until .

Q2 Dazzling Florist offers three sizes of flower arrangements containing roses, daisies and carnations during Mother’s Day. The owner of the florist noted that she used a total of 24 roses, 50 daisies and 48 carnations in filling orders for these three different types of flower arrangement sizes. Table Q2 below represents information regarding the flower arrangements:

Table Q2

ArrangementType Sizesof Flower

SmallArrangement

MediumArrangement

LargeArrangement

Total No.Of Flowers

Rose 1 2 4 24

Daisy 3 4 8 50

Carnation 3 6 6 48

By assuming number of small arrangement, number of medium arrangement

and number of large arrangement, the above problem can be formulated as

.

Determine the number of different arrangement sizes for each type of flower that Dazzling Florist made during Mother’s Day by using Doolittle factorization method.

This assignment is to be submitted on the fifth meeting (15 December 2012)


UNIVERSITI TUN HUSSEIN ONN MALAYSIABWM 21403 – MATEMATIK IV

GROUP 2 EE ASSIGNMENT NO.2

Q1 Find the root of that lies in the interval [-1, 0] by using

Bisection method. Iterate until .

Q2 A coffee merchant sells three blends of coffee. A bag of the house blend contains 300 grams of Colombian beans and 200 grams of French roast beans. A bag of the special blend contains 200 grams of Colombian beans, 200 grams of Kenyan beans and 100 grams of French roast beans. Meanwhile, a bag of the gourmet blend contains 100 grams of Colombian beans, 200 grams of Kenyan beans and 200 grams of French roast beans. The merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans and 25 kilograms of French roast beans.

By assuming number of bag of house blend, number of bag of special blend

and number of bag of gourmet blend, the above problem can be formulated as

.

Determine how many bags of each type of blend can be made if the merchant wishes touse up all of the beans by using Crout factorization method.




Q1 Find the root of that lies in the interval [2, 3] by using

Bisection method. Iterate until .

Q2 A biologist has placed three strains of bacteria (denoted I, II and III) in a test tube, where they will feed on three different food sources (A, B and C). Each day 200 units of A, 12,600 units of B and 5,950 units of C are placed in the test tube. Each bacteria consumes a certain number of units of each food per day, as shown in Table Q2 as follows:

Table Q2

Bacteria Strain I Bacteria Strain II Bacteria Strain III

Food A 1 1 1

Food B 40 60 80

Food C 20 25 40

By assuming as numbers of bacteria of Strain I, as numbers of bacteria of Strain II

and as numbers of bacteria of Strain III, the above problem can be formulated as

.

Determine the number of bacteria of each strain that can coexist in the test tube if they consume all of the food by using Doolittle factorization method.




Q1 Find the root of that lies in the interval [1.5, 2] by using Bisection


Q2 Ace Novelty wishes to produce three types of souvenirs: types A, B and C. During manufacturing process, a type-A souvenir requires 2 minutes on machine I, 1 minute on machine II and 2 minutes on machine III. A type-B souvenir requires 1 minute on machine I, 3 minutes on machine II and 1 minute on machine III. A type-C souvenir requires 1 minute on machine I and 2 minutes each on machine II and III. There are 3 hours available on machine I, 5 hours available on machine II and 4 hours available on machine II for processing the order.

By assuming number of Type A souvenir, number of Type B souvenir and

number of Type C souvenir, the above problem can be formulated as

.

Determine the number of each type should Ace Novelty make in order to use all of theavailable time by using Crout factorization method.




Q1 Find the root of that lies in the interval [1, 2] by using Bisection

method. Iterate until

Q2 A bakery produces cakes, doughnuts and muffins. Each cake requires 30 kg of flour, 21 kg of sugar and 12 kg of butter. Each doughnut requires 14, 12 and 6 kilograms of three ingredients, respectively. Finally, each muffin requires 8, 6 and 4 kilograms of these ingredients, respectively (refer to Table Q2 below).

Table Q2

Flour Sugar Butter

Cakes 30 21 12

Doughnuts 14 12 6

Muffins 8 6 4

Supplies of these ingredients vary from day to day, so the bakery needs to determine a different production run each day. There are 480 kg of flour, 360 kg of sugar and 200 kg of butter that available to be used. By assuming is the number of cakes to be baked,

is the number of doughnuts to be baked and is the number of muffins to be baked, the above problem can be formulated as


Find the number of cakes, doughnuts and muffins to be baked each day by using Doolittle factorization method.



Q1 Find the root of that lies in the interval [2, 3] by using Bisection


Q2 A mixture company has three sizes of packs of nuts. The Large size contains 2 kg of walnuts, 2 kg of peanuts and 1 kg of cashews. The Mammoth size contains 3 kg of walnuts, 6 kg of peanuts and 2 kg of cashews. The Giant size contains 1 kg of walnuts, 4 kg of peanuts and 2 kg of cashews. Suppose that the company receives an order for 14 kg of walnuts, 26 kg of peanuts and 12 kg of cashews.

By assuming as Large size of pack of nuts, as Mammoth size of pack of nuts and

as Giant size of pack of nuts, the above problem can be formulated as

.

Determine how can this company fill this order with the given sizes of packs by using Crout factorization method.

group asgmt no 2 ee

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