SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 2011

Size: px

Start display at page:

Download "SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 2011"

Iris Opal Short
5 years ago
Views:

1 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 (i) Populatio: Collectio of all possible idividual uits (persos, objects, experimetal outcome whose characteristics are to be studied) Sample: A part of populatio tha is studid to lear more about the etire populatio. (ii) Parameter: A quatitative measure that describes a characteristic of populatio. (iii) Statistics: A quatitative measure that describes a characteristic of a sample. Quatitative Data: Assume umerical values, which are ormally as a result of measuremets. Quatitative Data: Also kow as categorical data or attribute are data whose values fall ito oe or aother of a set of mutually exclusive ad exhaustive classes. (b) (i) Sturges Approximatio: K = +. log = 0 :. K = +. log 0.9 = (ii) Rage, R = Maximum observatio Miimum obersatio = 0 = 9 Class width, C = R = 9 = 9. = K Grouped Frequecy Distributio of Shoes Weight of Packet Tally Class width Frequecy Cumulative Frequecy Fix //// // //// //// //// //// / //// //// / //// //// //// // //// // //// // Mea = Σfx = =. Σf 0 Page of

2 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 Media = Lm + fcm Fm Cm Lm: Lower Class Boudary of the media class fcm : Cumulative frequecy just before media class fm: Frequecy of media class Cm: Class width of media class : Total frequecy Lm = 0.; fcm = ; fm = 9; = 0; Cm = :. Media = = =. = = Lo + C + Lo: Lower class boudary of model class : Absolute differece betwee frequecies of pre-model ad model classes : Absolute differece betwee frequecies of post-model ad model classes C: Class width of model class Lo = 0.; = = ; = \ = ; C = Mode = =. = (CAO) Page of

3 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 SOLUTION Vehicle Number 9 Age (x) Maiteace Cost (Y) χy Χ, ,00 0, Y = a + x, where b = ΣxY - Σx ΣY Σx (Σx ) = 09 - (0 x ) 0 - (0) = ˆ b = = 0 0 ^ b =.0 â = Y - bx ΣY - b Σx ^ =. - b 0 ˆ E x = 0 EY =,0 E xy =,09 E x = 0 ˆ Page of

4 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 â =. b, where b =.0 â =..0x â =. 0. â =. :. Y =. +.x (b) Maiteace Cost Table Years _ Module (x) Y =. +.0 x. +.0 (). +.0 (). +.0 (). +.0 (). +.0 (). +.0 (). +.0 (). +.0 () (9). +.0 () Maiteace Cost GHS (c) Estimate cost of maitaiig a year old vehicle _ Y =. +.0x, where x = _ Y =. +.0 () Y =. ^ Whe there is a chage i x, Y chage by b, where â is costat. SOLUTION (i) NPV is the preset value of cash flows mius the preset value of cash outflows NPV= Σ cash iflow at time t Σ Cash outflow at time t t = o (l + i) t (l + i) t t = o Page of

5 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 (ii) IRR is the iterest rate that causes the et preset value to equal l zero: NPV = Σ Net cashflow at time t t = o (l + IRR) t = o (b) (i) Let Cash Iflow = +, Cash outflow = - -0,000 -,000 -,000 Cash Flow,000,000,000,000,000 Time 0 = % = 0. (ii) NPV = Σ Cash Iflow at time t - Σ Cash Outflow at time t t = o ( +i) t t = o ( +i) t NPV =,000 +,000 +,000 +,000 +,000-0,000 -,000 -,000 (.) (.) (.) (.) (.) (.) (.) ALITER NET INFLOW - NET = NPV = = GHS, (iii) Yes, sice the NPV > 0 (c) (i) Net Cash Flow (GHS),000 -,00 Time 0 (ii) For IRR, NPV = 0 - NPV = Σ Net Cashflow at time t = 0 t = u ( + IRR) t Page of

6 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV = 0 ( + IRR) ( + IRR) 00 ( + IRR) - 0 = 0 ( + IRR) = 0 =. 00 = IRR = 0. or 0% SOLUTION (b) Task A B C D E F G H Preceedig Task - A A B C C D,E F Exepected completio time (9 + + ( X )) ( + + ( X ) Stadard deviatio of completio time (9 ) ( ) ( ) 0 / (c) 0 0 D B G A E 0. = C H F. (d) Critical path A, C F, H Earliest completio time 0./ weeks Page of

7 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 (e) Variace of critical path = ( / ) = /9 Stadard deviatio =. (f) Project completio time = weeks Stadard deviatio =. weeks Prob (less the 0 weeks) : 0 Z =. Z = 0. From ormal distributio tables P(Z < -0.) = = 0.9 SOLUTION Basic laws of Probability: - Multiplicative Law states that: If A ad B are idepedet evets the P(A B) = P(A)P(B) (i) If A ad B are depedet evets the P(A B) = P(A)P(B/A) = P(B)P(A/B) - Additive law states that: (i) If A ad B are evets the: P(A B) = P(A) + P(B) P(A B) If A ad B are mutually exclusive evets the P(A B) = P(A) + P(B) (b) Wuoyirie Veverie Zukyirie Total Outpatiet treatmet 0 Hospitalizatio Physicia s Bill 0 0 Total (i) Prob (bill is from Veverie cla) = 0 = 0. Page of

8 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 (ii) Prob (Hospitalizatio or Zukyirie cla) = Prob (Hospitalizatio) + P (Zukyirie cla) - (Hospitalizatio ad Zukyirie cla) = = = 0. (iii) P (Wuoyirie cla/hospitalizatio) = P (Hospitalizatio ad Wuoyirie cla) P (Hospitalizatio) = 0 0 = 0. (iv) Number of outpatiet from Wuoyirie or Zuleyirie = Total umber of patiets = 0 :. Pr Outpatiet from either Wuoyirie or Zuleyirie = 0 (v) Number of outpatiets or Physicia visitor from Veverie = 0 Total umber of patiets = 0 :. Outpatiet or visits Physicia from Veverie = 0 0 (vi) Number of hospitalized patiet from Veverie ad Wuoyirie = 0 :. Pr Hospitalized from Veverie ad Wuoyirie = 0 = 0 0 (vii) Number of patiets of the descriptio = = Total umber of patiets = 0 :. Pr Outpatiet from wuoyirie or Hospitalized from Veverie or visit Physicia ad from Zukyirie = 0 SOLUTION We use the least square liea regressio to fid the tred. Let y = a + bx, a ad b to be determied. Page of

9 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV x (quarters) Reveue (y) xy x Σx = 9 0 (b) Least square equatio): Σy = ax + b Σx : = a + b Σxy = a Σx + b Σx : 9 = a + 0b = 0b or b = = 0. 0 The a = () (0.) = 9. a =. :. Tredlie =. + 0.x (c) The tredlie. + 0.x used to do estimates: x (quarters) y (Reveue) Estimated Reveue Page 9 of Actual x 0% Estimate

10 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV : st Quarter Estimate = () = 9. d Quarter Estimate = () = 0. etc. (d) Averagig the % variatio for the quarters Q Q Q Q / / 0/ / Average Seasoal Variatios % 9% % 9% (e) Seasoally adjusted forecast = Tred Estimate x Seasoal Variatios % x (quarters) y (Reveue) Seasoally adjusted forecast Page of

11 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 (f) From the tredlie, the th quarter of 0 is obtaied as follows: Basic trd = () = 0.9 Seasoal adjustmet for th Quarter = 9% :. Adjusted Forecast = 0.9 x 9% =. SOLUTION Reasos iclude:. Protectio agaist delayed supply. Protectio agaist fluactuatig demad. Protectio agaist price chages (iflatio). Savigs or orderig cost. Beefits of large quatities discout (b) Assumptios are:. The demad for the item is costat over time.. Withi the rage of quatities to be ordered, the per uit holdig cost ad orderig cost are idepedet of the quatity ordered.. The repleishmet arrives exactly whe the ivetory level reaches zero. (c) (i) Demad (D) = GHS00.00 Orderig cost (K) = GHS.00 Holdig cost (H) = 0. (0%) EOQ = DK = x x 00 = 0,000 = GHS00 H 0. (ii) (ii) Aual demad GHS00.00 EOQ = GHS00.00 :. Number of times orders are placed i a year = D/EOQ = 00 =. times 00 Approximately times Total aual orderig cost = Number of orders i a year x orderig cost =. x = GHS0.00 Page of

12 SOLUTION QUANTITATIVE TOOLS IN BUSINESS NOV 0 (iii) Total aual holdig cost = HD = 0. x 00 = GHS0.00 (iv) If D quadruples from 00 to,000 the EOQ = x x 000 = = GHS00.00 EOQ douples from GHS00 to GHS00 ie GHS00 Page of

A random variable is a variable whose value is a numerical outcome of a random phenomenon.

A random variable is a variable whose value is a numerical outcome of a random phenomenon. The Practice of Statistics, d ed ates, Moore, ad Stares Itroductio We are ofte more iterested i the umber of times a give outcome ca occur tha i the possible outcomes themselves For example, if we toss