Math Paper

Derp university Derp derpington Human Resource Management Research Paper is Business Mathematics 101 1st Tri Semester SY 2011-2012 Ms. derpina derp TABLE OF circumscribe TITLE PAGE ACKNOWLEDGEMENTii TOPICS Simple Discount1 Simple Interest2 Four types of Interest available3 intensify Amount and Compound Interest4 Linear Programming Problems * Maximization6 * arcminuteimization8 Forecasting by Trend undertaking10 credit I would like to thank God for guiding and vainglorious me motivation to do this math research paper my friends for answering my questions about this paper Dr.Masajo for giving me the opportunity to gain more knowledge and my mother to constantly remind me to do better in college. I would like to thank my mentor, Ms. Grace Chong, for universe my mentor and to aid me in my college life. Simple Discount Find the present value of $3800 due in 6 months at 7% discount rate. A) F = $3800 d = 7% = . 07 t = 6 / 12 = 1/2 Formula D = Fdt Solution D = $3800 (. 07) (1/2) D = $1 33 P = F D P = $3800 $133 P = $3667 Discount $2056. 80 for 85 eld at a discount rate of 6 ? % B) F = 2056. 80 d = 6 ? % = . 065 t = 85 / 360 = 17 / 72 days Formula D = Fdt SolutionD = $2056. 80 (. 065) (17/72) D = $31. 57 P = F D P = $2056. 80 $31. 57 P = $2025. 13 Simple Interest Find simple following on $10,000 at the rate of 5% for 5 years. in like manner find the amount for 5 years. A) P = $10,000 R = 5% = . 05 T = 5 years = n = 5 I = PRT I = $10,000 (. 05) (5) I = $2500 A = P + I A = $10,000 + $2500 A = $12,500 Find simple pursuance on $15,600 for 1 ? years at the rate of 8% per annum. Also find total amount. B) P = $15,600 R = 8% = . 08 T = 1 ? = n = 1 ? I = PRT I = $15,600 (. 08) (1? ) I = $1872 A = P + I A = $15,600 + $1872 A = $17472 4 Types of Interest on hand(predicate)Find the different interest on $ jet at 6% from June 23 2011 to September 21 2015. A) Approximate number of days Year 2015 2011 = 4 Month 8 6 = 2 Days 51 23 = 28 4 x 360 = 1440 2 x 30 = 60 28 = 28 = 1528 Days B) Actual list of days 4 years x 365 days = 1463 days January 30 June 23 = 173 days January 30 September 21 = 263 days 1463 Days 173 days = 1287 days 1287 Days + 263 days = 1550 days = 1550 days C) Io interest for approximate number of days Io = PRT = $1000 (. 06) (1528/360) Io = $254. 67 D) Ie interest for approximate number of days Ie = PRT = $1000 (. 06) (1528/365) Ie = $251. 8 E) Io interest for actual number of days Io = PRT = $1000 (. 06) (1550/360) Io = $258. 33 F) Ie Interest for actual number of days Ie = PRT = $1000 (. 06) (1528/365) Ie = $254. 79 compound amount and Compounded interest Find the Compounded amount and compounded interest of $1000 at 7% for 3 years A) B) Compounded each year P = $1000 R = 7% = . 07 T = 3 years = N = 3 x 1 = 3 A = P (1+i) n A = $1000 (1+0. 7) 3 A = $1225. 043 I = A P I = $1225. 043 $1000 I = $225. 043 C) Compounded Semi Annually P = $1000 R = 7 / 2 % = 3. 5 = . 035 T = 3 years = N = 3 x 2 = 6 A = P (1+i) n A = $100 0 (1+0. 5) 6 A = $1229. 36 I = A P I = $1229. 36 $1000 I = $229. 36 D) Compounded quarterly P = $1000 R = 7 / 4% = 1. 75 = . 0175 T = 3 years = N = 3 x 4 = 12 A = P (1+i) n A = $1000 (1+0. 175) 12 A = $1231. 44 I = A P I = $1231. 44 $1000 I = $231. 44 E) Compounded Monthly P = $1000 R = 7 / 12% = . 5833 = . 00583 T = 3 years = N = 3 x 12 = 36 A = P (1+i) n A = $1000 (1+. 00583) 36 A = $1232. 78 I = A P I = $1232. 78 $1000 I = $232. 78 Compounded amount and Compounded interest Find the Compounded amount and compounded interest of $1500 at 5% for 3 years A) B) Compounded AnnuallyP = $1500 R = 5% = . 05 T = 3 years = N = 3 x 1 = 3 A = P (1+i) n A = $1500 (1+. 05) 3 A = $1736. 4375 I = A P I = $1736. 4375 $1500 I = $236. 4375 C) Compounded Semi Annually P = $1500 R = 5 / 2 % = 2. 5 = . 025 T = 3 years = N = 3 x 2 = 6 A = P (1+i) n A = $1500 (1+. 025) 6 A = $1739. 540127 I = A P I = $1739. 540127 $1500 I = $739. 540127 D) Compounded Quarterly P = $1500 R = 5 / 4% = 1 . 25 = . 0125 T = 3 years = N = 3 x 4 = 12 A = P (1+i) n A = $1500 (1+. 0125) 12 A = $1741. 131777 I = A P I = $1741. 131777 $1500 I = $741. 131777 E) Compounded Monthly P = $1500R = 5 / 12% = . 41666 = . 00416 T = 3 years = N = 3 x 12 = 36 A = P (1+i) n A = $1500 (1+. 00416) 36 A = $1741. 792 I = A P I = $1741. 792 $1500 I = $741. 792 Linear Programming Problems (Maximization) Levis Jeans manufacturing confederacy purchase2 personal manners of jeans, style X and style Y, which sell for $90 and $75 appropriately. Unit production test for style X is $40 and for style Y $35. raw materials available monthly are 90 meters while processing time at a max of 70 hours per week. Style X jeans made 3 meters of materials and 2 for processing them. For style Y, 2 meters and 2 for processing.Style X market demand is no more than 40 per week. How many of each style should be produced in each week in order to make profit maximum? Style X Style Y Total Available RM 3 2 90 PT 2 2 70 MD 4 0 Style X Style Y USP $90 $75 UPE 40 35 UBM $50 $40 Composition of linear programming problems I. Decision Variable X = Number of style X to be produced periodical Y = Number of style Y to be produced weekly II. Objective Function Maximum Profit (Z) Z = $50X+$40Y III. Subjects & Constraints RM = 3X+2Y 90PT = 2X+2Y 70 MD = X 40X Y 0 IV. Graphical SolutionsA) By intercept B) Graphical presentations and points A intersection between 2 lines C) Testing the curve of the convex polygon make watered form the objective function V. Decision Raw Materials 3X+2Y 90 X = 30 Y = 45 Processing Time 2X+2Y 70 X = 35 Y = 35 Market Demand X = 40 A) Z = $50X + $40Y = $50(0) + $40(35) =$1400 B) Z = $50X + $40Y = $50(20) + $40(75) =$1600 C) Z = $50X + $40Y = $50(30) + $40(0) =$1500 Choose B. Decision The Levis manufacturing company must produce 20 pieces of style X and 50 pieces of style Y to have a maximum profit of $1600. Linear Programming Problems (Minimization)Mrs. Smith mining company ow ns ii mines grading ores graded into 3 classes. High grade (H), Medium grade (M) and low grade (L). The company is tied with a contract to provide a smelting plant with 12 tons of (H), 8 tons of (M), and 24 tons of (L) per week. It costs $2000 per day to run mine 1 and $1600 per day to run mine 2. In a day operation, Mine 1 produces 6 tons of (H), 2 tons of (M) and 4 tons of (L). While mine 2 produces 2 tons of (H) 2 tons of (M) and 12 tons of (L). How many days a week should each mines operation to fulfil companys allegiance most economically? Mine 1 Mine 2 Total AvailableH 6 2 12 M 2 2 8 L 4 12 24 Cost $2000 $1600 I. Decision Variables X = Number of days to run mine 1 Y = Number of days to run mine 2 II. Objective Functions Minimum Cost = $2000X + $1600Y III. Subjects to Constraints H = 6X + 2Y 12 M = 2X + 2Y 8 L = 4X + 12Y 24 X Y 0 IV. Graphical Solutions H = 6X + 2Y 12M = 2X + 2Y 8L = 4X + 12Y 24 X = 2 Y = 6X = 4 Y = 4X = 6 Y = 2 P1 (0,6) Min C = $2000(0) + $1600(6) = $9600 P2 (1,3) Min C = $2000(1) + $1600(3) = $6800 P3 (3,1) Min C = $2000(3) + $1600(1) = $7600 P4 (6,0) Min C = $2000(6) + $1600(0) = $12000Choose P2 V. Decision Mrs. Smiths mining company should run mine 1 for 1 day and Mine 2 for 3 days in order to have a minimum cost of $6800. Forecasting by Trend Projection Forecast and graph the production of rice in the Philippines for the years 2012 and 2015 of the annual production of rice from year 2000 to year 2010. Year (N) Production of Rice (Y) X XY Y X2 2000 20 0 0 0 2001 22 1 22 1 2002 18 2 36 4 2003 19 3 57 9 2004 21 4 84 16 2005 24 5 120 25 2006 22 6 132 36 2007 26 7 182 49 2008 28 8 224 64 2009 25 9 225 81 010 30 10 300 100 ? (Y) = 255 ? (X) = 55 ? (XY)=1382 ? (X2) = 385 2 Normal Equations ?(Y) = NA + B? (X)Equation 1 ?(XY) = A? (X) + B? (X2)Equation 2 Solve for B) 255 = 11A + 55B (-5) 1382 = 55A + 385B -1275 = -55A 275B 1382 = 55A + 385B 107 /100 = 110B /100 B = . 97272727 Solve for A) 255 = 11A + 55B 11A + 55B = 2 55 11A +55(. 97272727) = 255 11A + 53. 5 = 255 11 A = 255 53. 5 11A /11 = 201. 5 /11 A = 18. 31818182 A = 18. 32 B = 0. 97 Formula Y = A+Bx Year 2000 = 18. 32 + 0. 97(0) Y = 18. 32 Year 2001 = 18. 32 + 0. 97(1) Y = 19. 29 Year 2002 = 18. 32 + 0. 92(2) Y = 20. 6 Year 2003 = 21. 23 Year 2004 = 22. 2 Year 2005 = 23. 17 Year 2006 = 24. 14 Year 2007 = 25. 11 Year 2008 = 26. 08 Year 2009 = 27. 05 Year 2010 = 28. 02 In the table Year (N) Production of Rice (Y) X XY Y X2 2000 20 0 0 18. 32 0 2001 22 1 22 19. 29 1 2002 18 2 36 20. 26 4 2003 19 3 57 21. 23 9 2004 21 4 84 22. 2 16 2005 24 5 120 23. 17 25 2006 22 6 132 24. 14 36 2007 26 7 182 25. 11 49 2008 28 8 224 26. 08 64 2009 25 9 225 27. 05 81 2010 30 10 300 28. 02 100 ? (Y) = 255 ? (X) = 55 ? (XY)=1382 ? (X2) = 385