answers of the problems Q.1. Consider an unknown system with two inputs, x1, x2 , and one output, y, as shown in the following Figure 1a. Let inputs x1 be within the range X1 = [0,20] and x2 in X2 = [0,10]. Suppose that X1 has two associate membership functions, µS1(.) and µL1(.), describing “small” and “large,” respectively, and similarly X2 has µS2(.) and µ L2(.), as shown in Figure 2 (b)-(c). Now, suppose that we know, from experiments, the following input-output relations (fuzzy IF-THEN implication rules): R1: IF x1 is small AND x2 is small THEN y = x1 + x2 R2: IFx1 is large THEN y = 1/2 x1 R3: IFx2 is large THEN y = 1/3 x2. Otherwise, y = 0. Let 0 x01 = 15 and x20 = 5 be given; a) Calculate the fuzzy membership values of the outputs. (10-Marks) b) Calculate the average value of the final output, corresponding to the input.(20-Marks) c) Calculate the three membership functions, one “small” and two “large,” for the final output. (20-Marks) Figure 1 Figure 2 Q.2. A manufacturing company produces 3 product types. The products are made of number of subassemblies and components. The bill-of materials (BOM) of these three products are depicted in the following figure. The numbers in the parentheses indicate the number of component needed for each unit of item to make one unit of upper level subassembly. (3) (2) (3) (5) (4) (2) (3) (5) (2) (2) (4) (4) (5) (2) (2) The company wants to plan the next 6 months period. The expected demands in the next six months are estimates as: Product Type 1 2 3 4 5 6 A 300 250 400 150 350 475 B 200 300 250 600 550 375 C 500 350 450 550 300 650 Total 1000 900 1100 1300 1200 1500 The company employs 20 people. The number of workable days in next six months are as follows: Months 1 2 3 4 5 6 Days 22 21 23 22 23 23 The company further uses overtime, subcontractor and part-time worker if necessary to meet the demand within the time period. However, if it is not possible to meet the demand within the period then the company uses backlog option. The related company capacity is given below: Regular time production : 2 unit/day/per worker Overtime production : 1 unit/day/per worker Subcontractor capacity : 75 units/per month Part time worker capacity : 1 unit/day/per worker The company does not use part-time worker in overtime period and does not use more than 10 working days for the overtime in a month. The company sees a great benefit in reverse logistics and encourages its distributors and customers to return the products that have completed their economic lives, to the company. The previous experience show that the expected number of return items in next six periods would be: Product Type P 1 E 2 R 3 I 4 O 5 D 6 A 30 50 40 30 25 50 B 40 40 30 20 25 50 C 20 25 30 50 25 20 Total 90 115 100 100 75 120 Yet again, the past experience indicate that the refurbishable/repairable/reusable product rate is on average 50% and the remaining 50% is disposed. However, the company realised that on average 20% of disposable products has some parts that are intact and with minor refurbishments these can be used in remanufacturing. These components belong to subassemblies A3, ß, and II. Any full-time worker can refurbish/repair/reuse 4 units of returned products during normal working times and 2 returned products in overtime period if necessary. Further, 6 units of A1, or A2, or p, or I or Z subassembly components can be manufactured and assembled by a FT worker in a normal time if needed. These parts are not manufactured in overtime period. Neither subcontractor nor PT worker is used in component manufacturing separately. The relevant cost figures are given below: Costs Output Regular Time =$7 per unit Overtime =$10 per unit Subcontract =$15 per unit Regular time cost of individual component production = $3/per unit Inventory =$10 per unit per period on average inventory Backorders =$20 per unit per period Returned Items cost at regular time Cost of recycling =$1/per unit Disassembly & Repair cost =$2/ per unit Maintenance cost =$1/ per unit Disposal cost =$0.5/ per unit Overtime cost of returned items Disassembly & Repair cost =$2.5/ per unit Maintenance cost =$1.5/ per unit Prepare an Aggregate plan using different combinations of available capacity for this company for the next six months. (50-Marks) 3. Maeda Company has the following employees on payroll 1. Maeda Company has the following employees on thepayroll: Employee Name Amal Miguel Byron Hiroko Marital Semimonthly Witholding Status Payroll Allowances S M S M Using the information above: $4,000 $5,000 $4,600 $6,500 1 3 2 4 a. Calculate the FUTA tax liability for 2013. Assume that Maeda Company has paid all amounts due during the year. b. If the payroll is consistent from quarter to quarter, how much would be remitted in FUTA taxes in each of the four quarters in 2013? 2. Quince Company has book income of $120,000 properly determined in accordance with financial accounting principles. The following information is also available: • The company received a $10,000 dividend from a large publicly-traded domestic corporation of which it owns less than 20%. • Income tax expense on the financial statements was $30,000. • Depreciation expense on the financial statements is $25,000 less than depreciation expense determined using tax laws. • The company received life insurance proceeds of $15,000. • Charitable contributions of $20,000 were made. Determine the taxable income of Quince Company. vc, Lu we rubric below for the grading criteria for this assignment. CATEGORY Tax Liability (20 Points) Quarterly Tax (20 Points) Exemplary 20 points Satisfactory Student provides a correct calculation of the FUTA tax liability for 2013. Taxable income (35 Points) 20 points Student provides a correct calculation of FUTA taxes in each of the four quarters of 2013. 35 points Student provides a correct calculation of Quince Company’s taxable income. 15 points Student provides a mostly correct calculation of the FUTA tax liability for 2013. 15 points Student provides a mostly correct calculation of FUTA taxes in each of the four quarters of 2013. Unsatisfactory 10 points Student provides a partially correct calculation of the FUTA tax liability for 2013. 26 points Student provides a mostly correct calculation of Quince Company’s taxable income. 10 points Student provides a partially correct calculation of FUTA taxes in each of the four quarters of 2013. 17 points Student provides a partially correct calculation of Quince Company’s taxable income. Unacceptable 5 points Student provides a poor or incorrect calculation of the FUTA tax liability for 2013. 5 points Student provides a poor or incorrect calculation of FUTA taxes in each of the four quarters of 2013. 8 points Student provides a poor or incorrect calculation of Quince Company’s taxable income. Mechanics -Grammar, Punctuation, Spelling (10 Points Format – APA Format, Citations, Organization, Transitions (15 Points) 10 points Student does not make any errors in grammar or spelling, especially those that distract the reader from the content. 15 points The paper is written in proper APA and organizational format. All sources used for quotes and facts are credible and cited correctly. Excellent organization, including a variety of thoughtful transitions. 8 points Student makes 1-2 errors in grammar or spelling that distract the reader from the content. 5 points Student makes 3-4 errors in grammar or spelling that distract the reader from the content. 2 points Student makes more than 4 errors in grammar or spelling that distract the reader from the content. 12 points The paper is written in proper format with only 1-2 errors. All sources used for quotes and facts are credible, and most are cited correctly. Adequate organization includes a variety of appropriate transitions. 8 points The paper is written in proper format with only 3-5 errors. Most sources used for quotes and facts are credible and cited correctly. Essay is poorly organized, but may include a few effective transitions. 5 points The paper is not written in proper format. Many sources used for quotes and facts are less than credible (suspect) and/or are not cited correctly. Essay is disorganized and does not include effective transitions.

answers of the problems

Q.1.  Consider an unknown system with two inputs, x1, x2 , and one output, y, as shown in the following Figure 1a.  Let inputs x1 be within the range X1 = [0,20] and x2 in X2 = [0,10]. Suppose that X1 has two associate membership functions, µS1(.) and µL1(.), describing “small” and “large,” respectively, and similarly X2 has µS2(.) and µ L2(.), as shown in Figure 2 (b)-(c).  Now, suppose that we know, from experiments, the following input-output relations (fuzzy IF-THEN implication rules):
R1: IF x1 is small AND x2 is small THEN y = x1 + x2
R2: IFx1 is large THEN y = 1/2 x1
R3: IFx2 is large THEN y = 1/3 x2.
Otherwise, y = 0.
Let 0  x01 = 15 and x20 = 5 be given;
a)    Calculate the fuzzy membership values of the outputs.              (10-Marks)
b)    Calculate the average value of the final output, corresponding to the input.(20-Marks)
c)    Calculate the three membership functions, one “small” and two “large,” for the final output.                                           (20-Marks)

Figure 1

Figure 2

Q.2. A manufacturing company produces 3 product types. The products are made of number of subassemblies and components. The bill-of materials (BOM) of these three products are depicted in the following figure. The numbers in the parentheses indicate the number of component needed for each unit of item to make one unit of upper level subassembly.

(3)           (2)                 (3)               (5)                            (4)                  (2)    (3)                (5)          (2)

(2)        (4)                 (4)         (5)           (2)                (2)
The company wants to plan the next 6 months period. The expected demands in the next six months are estimates as:
Product Type
1
2
3
4
5
6
A    300    250    400    150    350    475
B    200    300    250    600    550    375
C    500    350    450    550    300    650
Total    1000    900    1100    1300    1200    1500

The company employs 20 people. The number of workable days in next six months are as follows:
Months    1    2    3    4    5    6
Days    22    21    23    22    23    23

The company further uses overtime, subcontractor and part-time worker if necessary to meet the demand within the time period. However, if it is not possible to meet the demand within the period then the company uses backlog option.
The related company capacity is given below:

Regular time production     : 2 unit/day/per worker
Overtime production    : 1 unit/day/per worker
Subcontractor capacity    : 75 units/per month
Part time worker capacity    : 1 unit/day/per worker
The company does not use part-time worker in overtime period and does not use more than 10 working days for the overtime in a month.
The company sees a great benefit in reverse logistics and encourages its distributors and customers to return the products that have completed their economic lives, to the company. The previous experience show that the expected number of return items in next six periods would be:
Product Type    P
1    E
2    R
3    I
4    O
5    D
6
A    30    50    40    30    25    50
B    40    40    30    20    25    50
C    20    25    30    50    25    20
Total    90    115    100    100    75    120

Yet again, the past experience indicate that the refurbishable/repairable/reusable product rate is on average 50% and the remaining 50% is disposed. However, the company realised that on average 20% of disposable products has some parts that are intact and with minor refurbishments these can be used in remanufacturing. These components belong to subassemblies A3, ß, and II.
Any full-time worker can refurbish/repair/reuse 4 units of returned products during normal working times and 2 returned products in overtime period if necessary. Further, 6 units of A1, or A2, or p,  or I  or Z subassembly components can be manufactured and assembled by a FT worker in a normal time if needed. These parts are not manufactured in overtime period. Neither subcontractor nor PT worker is used in component manufacturing separately.
The relevant cost figures are given below:
Costs
Output
Regular Time         =$7 per unit
Overtime         =$10 per unit
Subcontract         =$15 per unit
Regular time cost of individual component production = $3/per unit
Inventory             =$10 per unit per period on average inventory
Backorders             =$20 per unit per period

Returned Items cost at regular time
Cost of recycling        =$1/per unit
Disassembly & Repair cost    =$2/ per unit
Maintenance cost        =$1/ per unit
Disposal cost            =$0.5/ per unit
Overtime cost of returned items
Disassembly & Repair cost    =$2.5/ per unit
Maintenance cost        =$1.5/ per unit
Prepare an Aggregate plan using different combinations of available capacity for this company for the next six months.
(50-Marks)

3. Maeda Company has the following employees on payroll

1. Maeda Company has the following employees on thepayroll:
Employee Name
Amal Miguel Byron Hiroko
Marital Semimonthly Witholding Status Payroll Allowances
S M
S
M
Using the information above:
$4,000 $5,000 $4,600 $6,500
1
3
2
4
a. Calculate the FUTA tax liability for 2013. Assume that Maeda Company has paid all amounts due during the year.
b. If the payroll is consistent from quarter to quarter, how much would be remitted in FUTA taxes in each of the four quarters in 2013?
2. Quince Company has book income of $120,000 properly determined in accordance with financial accounting principles. The following information is also available: • The company received a $10,000 dividend from a large publicly-traded domestic corporation of which it owns less than 20%. • Income tax expense on the financial statements was $30,000. • Depreciation expense on the financial statements is $25,000 less than depreciation expense determined using tax laws. • The company received life insurance proceeds of $15,000. • Charitable contributions of $20,000 were made.
Determine the taxable income of Quince Company.

vc, Lu we rubric below for the grading criteria for this assignment.
CATEGORY
Tax Liability (20 Points)
Quarterly Tax (20 Points)
Exemplary
20 points
Satisfactory
Student provides a correct calculation of the FUTA tax liability for 2013.
Taxable income (35 Points)
20 points
Student provides a correct calculation of FUTA taxes in each of the four quarters of 2013. 35 points Student provides a correct calculation of Quince Company’s taxable income.
15 points Student provides a mostly correct calculation of the FUTA tax liability for 2013.
15 points Student provides a mostly correct calculation of FUTA taxes in each of the four quarters of 2013.
Unsatisfactory 10 points Student provides a partially correct calculation of the FUTA tax liability for 2013.
26 points Student provides a mostly correct calculation of Quince Company’s taxable income.
10 points Student provides a partially correct calculation of FUTA taxes in each of the four quarters of 2013.  17 points Student provides a partially correct calculation of Quince Company’s taxable income.
Unacceptable 5 points Student provides a poor or incorrect calculation of the FUTA tax liability for 2013. 5 points Student provides a poor or incorrect calculation of FUTA taxes in each of the four quarters of 2013.
8 points Student provides a poor or incorrect calculation of Quince Company’s taxable income.
Mechanics -Grammar, Punctuation, Spelling (10 Points
Format – APA Format, Citations, Organization, Transitions (15 Points)
10 points Student does not make any errors in grammar or spelling, especially those that distract the reader from the content.
15 points The paper is written in proper APA and organizational format. All sources used for quotes and facts are credible and cited correctly. Excellent organization, including a variety of thoughtful transitions.
8 points Student makes 1-2 errors in grammar or spelling that distract the reader from the content.
5 points Student makes 3-4 errors in grammar or spelling that distract the reader from the content.
2 points Student makes more than 4 errors in grammar or spelling that distract the reader from the content.
12 points The paper is written in proper format with only 1-2 errors. All sources used for quotes and facts are credible, and most are cited correctly. Adequate organization includes a variety of appropriate transitions.
8 points The paper is written in proper format with only 3-5 errors. Most sources used for quotes and facts are credible and cited correctly. Essay is poorly organized, but may include a few effective transitions.
5 points The paper is not written in proper format. Many sources used for quotes and facts are less than credible (suspect) and/or are not cited correctly. Essay is disorganized and does not include effective transitions.