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Financial Management (E. Quantitative Methods)E. QUANTITATIVE METHODSTHEORIES:Economic Order Quantity The economic order quantity is the order quantity that results in A. the minimum total annual inventory costs. B. no inventory shortages. C. the maximum total annual inventory costs. D. minimum orde...

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Fi nanc i alManagement ( E.Quant i t at i veMe t hods)

E. QUANTI T ATI VEMETHODS

A.PERTu s e sp r o b a b i l i t yd i s t r i b u t i o no nt h ea c t i v i t yt i me swh i l eCPMu s e sp o i n t e s t i ma t e sf o r t h ea c t i v i t yt i me s . B. PERTd o e sn o t a l l o wf o rs l a c kt i me so nt h ea c t i v i t i e swh i l eCPMd o e s . C.PERTc o n s i d e r so n l ya c t i v i t yc o s t wh i l eCPMc o n s i d e r so n l ya c t i v i t yt i me . D.PERTd e t e r mi n e st h el e a s t c o s tp a t ht h r o u g han e t wo r kwh i l eCPMd e t e r mi n e st h el e a s t t i mep a t ht h r o u g han e t wo r k .

THEORI ES: Ec on o mi cOr d e rQu a nt i t y 1 .T h ee c o n o mi co r d e rq u a n t i t yi st h eo r d e rq u a n t i t yt h a t r e s u l t si n A.t h emi n i mu mt o t a l a n n u a l i n v e n t o r yc o s t s . B.n oi n v e n t o r ys h o r t a g e s . C.t h ema x i mu mt o t a l a n n u a l i n v e n t o r yc o s t s . D.mi n i mu mo r d e r i n gc o s t s .

6 . Cr i t i c a lPa t hMe t h o d( CPM)i sat e c h n i q u ef o ra n a l y z i n g ,p l a n n i n g ,a n ds c h e d u l i n gl a r g e , c o mp l e xp r o j e c t sb yd e t e r mi n i n gt h ec r i t i c a l p a t hf r o mas i n g l et i mee s t i ma t ef o re a c he v e n t i nap r o j e c t .T h ec r i t i c a l p a t h : A.I st h es h o r t e s t p a t hf r o mt h efi r s t e v e n t t ot h el a s t e v e n t f o rap r o j e c t . B.I sa na c t i v i t ywi t h i nt h ep a t ht h a t r e q u i r e st h emo s t n u mb e ro f t i me . C.Ha sc o mp l e t i o nt h a t r e fl e c t st h ee a r l i e s t t i met oc o mp l e t et h ep r o j e c t . D.I st h ema x i mu ma mo u n to ft i mea na c t i v i t yma yb ed e l a y e dwi t h o u td e l a y i n gt h et o t a l p r o j e c t b e y o n di t st a r g e t c o mp l e t i o nt i me .

Se n s i t i v i t ya n a l y s i s 2 . Mi s s i l eCo mp a n yh a sc o r r e c t l yc o mp u t e di t se c o n o mi co r d e rq u a n t i t ya s5 0 0u n i t s .Ho we v e r , ma n a g e me n tf e e l si two u l dr a t h e ro r d e rq u a n t i t i e so f6 0 0u n i t s .Ho ws h o u l dMi s s i l e ’ st o t a l a n n u a l p u r c h a s e o r d e rc o s t sa n dt o t a l a n n u a l c a r r y i n gc o s tf o ra no r d e rq u a n t i t yo f6 0 0u n i t s c o mp a r et ot h er e s p e c t i v ea mo u n t sf o ra no r d e rq u a n t i t yo f 5 0 0u n i t s ? A.Hi g h e rp u r c h a s e o r d e rc o s t a n dl o we rc a r r y i n gc o s t . B. Hi g h e rp u r c h a s e o r d e rc o s t a n dh i g h e rc a r r y i n gc o s t . C.L o we rp u r c h a s e o r d e rc o s t a n dh i g h e rc a r r y i n gc o s t . D.L o we rp u r c h a s e o r d e rc o s t a n dl o we rc a r r y i n gc o s t .

Qu e ui n gT he or y 7 . Ac o mp a n yi sd e s i g n i n gan e wr e g i o n a ld i s t r i b u t i o nwa r e h o u s e .T omi n i mi z ed e l a y si n l o a d i n ga n du n l o a d i n gt r u c k s , a na d e q u a t en u mb e ro f l o a d i n gd o c k smu s t b eb u i l t .Th emo s t r e l e v a n t t e c h n i q u et oa s s i s t i nd e t e r mi n i n gt h ep r o p e rn u mb e rd o c k si s A.Co s t v o l u me p r o fi t a n a l y s i s C.L i n e a rp r o g r a mmi n g D.Qu e u i n gt h e o r y B.PERT/ CPMa n a l y s i s

3 . Ad e c r e a s ei ni n v e n t o r yo r d e rc o s t swi l l A.I n c r e a s et h er e o r d e rp o i n t . B. De c r e a s et h ee c o n o mi co r d e rq u a n t i t y . C.Ha v en oe ff e c t o nt h ee c o n o mi co r d e rq u a n t i t y . D.De c r e a s et h eh o l d i n gc o s t p e r c e n t a g e .

L i n e a rPr og r a mmi ng Us et h ef o l l o wi n gi n f o r ma t i o nt oa n s we rq u e s t i o nNo s . 8a n d9 : T h eKi n i sCo mp a n yp r o d u c e sac o s me t i cp r o d u c t i n6 0g a l l o nb a t c h e s .Th eb a s i ci n g r e d i e n t su s e d a r ema t e r i a l X, c o s t i n gP7 0p e rg a l l o n , a n dma t e r i a l Y , c o s t i n gP1 7 0p e rg a l l o n .Nomo r et h a n1 8 g a l l o n so f Xc a nb eu s e d , a n da t l e a s t 1 5g a l l o n so f Ymu s t b eu s e d .

4 . Ani n c r e a s ei ni n v e n t o r yh o l d i n gc o s t swi l l A.De c r e a s et h ee c o n o mi co r d e rq u a n t i t y . B. Ha v en oe ff e c t o nt h ee c o n o mi co r d e rq u a n t i t y . C.I n c r e a s et h ee c o n o mi co r d e rq u a n t i t y . D.De c r e a s et h en u mb e ro f o r d e r si s s u e dp e ry e a r .

8 . Ho wwo u l dt h eo b j e c t i v ef u n c t i o n( mi n i mi z a t i o no f p r o d u c t c o s t )b ee x p r e s s e d ? A.7 0 X+1 7 0 Y C.1 7 0 X+7 0 Y B. 1 8 X+1 5 Y D.1 8 X+4 2 Y

PERT CPM 5 . Wh i c ho n eo ft h ef o l l o wi n gs t a t e me n t sb e s td e s c r i b e sad i ff e r e n c eb e t we e nb a s i cPERTa n d t h eCr i t i c a l Pa t hMe t h o d( CPM)o f n e t wo r ka n a l y s i s ? 714

9 . Wh i c ho f t h ef o l l o wi n gi sn o t ac o n s t r a i n t o f t h eKi n i sCo mp a n y ? A.X≤1 8 C.Y≥1 5 B. X+Y≤6 0 D.X≥0

Fi nanc i alManagement ( E.Quant i t at i veMe t hods)

Ca s t l ed e s i r e st or e d u c et h en o r ma l c o mp l e t i o nt i meo f J o bWW a n d , a t t h es a met i me , r e p o r t t h eh i g h e s t p o s s i b l ei n c o mef o rt h ey e a r .Ca s t l es h o u l dc r a s h A.Ac t i v i t yBC1we e ka n da c t i v i t yEF1we e k B. Ac t i v i t yBC2we e k s C.Ac t i v i t yDE1we e ka n da c t i v i t yBC1we e k D.Ac t i v i t yDE1we e ka n da c t i v i t yE F1we e k

Us et h ef o l l o wi n gd a t at oa n s we rQu e s t i o nNo s . 1 0t h r o u g h1 2 :

Sun, Inc. manufactures product X and product Y, which are processed as follows: Pr o d u c t X Pr o d u c t Y

T y p eAma c h i n e 6h o u r s 9h o u r s

T y p eBma c h i n e 4h o u r s 5h o u r s

L e a r n i n gCur v e 1 . Co n t r a t i s t a ,I n c .i sc o n s i d e r i n gat h r e e p h a s er e s e a r c hp r o j e c t .T h et i mee s t i ma t e sf o r c o mp l e t i o no f Ph a s e2o f t h ep r o j e c t a r e : Pe s s i mi s t i c 2 4we e k s Mo s t l i k e l y 2 0we e k s Op t i mi s t i c 1 0we e k s Us i n gt h ep r o g r a me v a l u a t i o na n dr e v i e wt e c h n i q u e( PERT) ,t h ee x p e c t e dt i me f o r c o mp l e t i o no f Ph a s e2s h o u l db e A.2 0we e k s C.1 8we e k s B.1 9we e k s D.2 4we e k s

T h ec o n t r i b u t i o nma r g i ni sP1 2f o rp r o d u c tXa n dP7f o rp r o d u c tY .Th ea v a i l a b l et i med a i l yf o r p r o c e s s i n gt h et wop r o d u c t si s1 2 0h o u r sf o rma c h i n eT y p eAa n d8 0h o u r sf o rma c h i n eT y p eB. 1 0 .Ho wwo u l dt h ec o n s t r a i n t f o rma c h i n eT y p eAb ee x p r e s s e d ? A.4 X+5 Y C.4 X+5 Y≤8 0 B. 6 X+9 Y≤1 2 0 D.1 2 X+7 Y 1 1 .Ho wwo u l dt h ec o n s t r a i n t f o rma c h i n eT y p eBb ee x p r e s s e d ? A.4 X+5 Y C.4 X+5 Y≤8 0 B. 6 X+9 Y≤1 2 0 D.1 2 X+7 Y

2

. Wi n dCo mp a n ye x p e c t sa n8 5 %l e a r n i n gc u r v e .T h efi r s t b a t c ho f an e wp r o d u c t r e q u i r e d5 0 0 h o u r s .T h efi r s t f o u rb a t c h e ss h o u l dt a k ea na v e r a g eo f A.3 6 1 . 2 5h o u r s C.5 0 0 . 0h o u r s B. 4 2 5 . 0h o u r s D.3 2 2 . 4h o u r s

1 2 .Ho wwo u l dt h eo b j e c t i v ef u n c t i o nb ee x p r e s s e d ? A.4 X+5 Y C.4 X+5 Y≤8 0 B. 6 X+9 Y≤1 2 0 D.1 2 X+7 Y

3

. Al e a r n i n gc u r v eo f8 0 %a s s u me st h a tp r o d u c t i o nu n i tc o s t sa r er e d u c e db y2 0 %f o re a c h d o u b l i n go fo u t p u t . Wh a ti st h ec o s to ft h es i x t e e n t hu n i tp r o d u c e da sa na p p r o x i ma t e p e r c e n t o f t h efi r s t u n i t p r o d u c e d ? A.3 0p e r c e n t C.4 1p e r c e n t B.5 1p e r c e n t D.6 4p e r c e n t

PROBL EMS: PERT CPM

2. Castle Building Company uses the critical path method to monitor construction jobs. The company is currently 2 weeks behind schedule on Job WW, which is subject to a P10,500-per-week completion penalty. Path A-BC-F-G-H-I has a normal completion time of 20 weeks, and critical path A-DE-F-G-H-I has a normal completion time of 22 weeks. The following activities can be crashed. Ac t i v i t i e s BC DE EF

Co s t t oCr a s h1We e k P8 , 0 0 0 1 0 , 0 0 0 8 , 8 0 0

4

. So f t I n c . h a sat a r g e t t o t a l l a b o rc o s to f P3 , 6 0 0f o rt h efi r s t f o u rb a t c h e so fap r o d u c t .L a b o r i sp a i dP1 0a nh o u r .I f So f t e x p e c t sa n8 0 %l e a r n i n gc u r v e , h o wma n yh o u r ss h o u l dt h efi r s t b a t c ht a k e ? A.3 6 0h o u r s C.5 7 . 6h o u r s B.1 4 0 . 6 3h o u r s D.2 3 0 . 4h o u r s

Co s t t oCr a s h2We e k s P1 5 , 0 0 0 1 9 , 6 0 0 1 9 , 5 0 0

5

. Ha v e n o th a se s t i ma t e dt h efi r s tb a t c ho fp r o d u c twi l lt a k e4 0h o u r st oc o mp l e t e . A9 0 %

715

Fi nanc i alManagement ( E.Quant i t at i veMet hods)

* Ap p l i e da t t h er a t eo f 1 0 %o f v a r i a b l ec o s t . T h ec o mp a n yh a sn o wb e e nr e q u e s t e dt op r e p a r eab i df o r1 5 0u n i t so f t h es a mep r o d u c t . I fa n8 0p e r c e n tl e a r n i n gc u r v ei sa p p l i c a b l e ,Mo s sPo i n t ’ st o t a l c o s to nt h i so r d e rwo u l db e e s t i ma t e da t A.P2 6 , 4 0 0 C.P3 1 , 7 9 0 B.P3 7 , 9 5 0 D.P3 8 , 5 0 0

l e a r n i n gc u r v ei se x p e c t e d .I f l a b o ri sp a i dP1 5p e rh o u r , t h et a r g e t l a b o rc o s t f o rf o u rb a t c h e s o f p r o d u c t i s C.P1 , 9 4 4 A.P6 0 0 B. P2 , 1 6 0 D.P2 , 4 0 0 6

. Ha n i pCo .u s e d3 0h o u r st op r o d u c et h efi r s tb a t c ho fu n i t s .T h es e c o n db a t c ht o o ka n a d d i t i o n a l 1 8h o u r s .Ho wma n yt o t a l h o u r swi l l t h efi r s t f o u rb a t c h e sr e q u i r e ? A.7 6 . 8h o u r s C.1 2 0 . 0h o u r s B. 9 6 . 2h o u r s D.4 8 . 0h o u r s

7

. Su l i t Co mp a n yp l a n st ob e g i np r o d u c t i o no f an e wp r o d u c t o nJ u l y1 .An8 0 %l e a r n i n gc u r v ei s a p p l i c a b l et oSu l i t ’ sma n u f a c t u r i n go p e r a t i o n s .I f i t i se x p e c t e dt ot a k e1 , 0 0 0d i r e c t l a b o rh o u r s t op r o d u c et h efi r s tu n i t ,h o wma n yd i r e c tl a b o rh o u r ss h o u l di tt a k et op r o d u c et h et h i r da n d f o u r t hu n i t s ? A.6 4 0 C.1 , 6 0 0 B. 9 6 0 D.2 , 5 6 0

Ex p e c t e dV a l u e 1 0

. Dough Distributors has decided to increase its daily muffin purchases by 100 boxes. A box of muffins costs P2 and sells for P3 through regular stores. Any boxes not sold through regular stores are sold through Dough’s thrift store for P1. Dough assigns the following probabilities to selling additional boxes: Ad d i t i o n a l s a l e s Pr o b a b i l i t y 6 0 0 . 6 1 0 0 0 . 4 Wh a t i st h ee x p e c t e dv a l u eo f Do u g h ’ sd e c i s i o nt ob u y1 0 0a d d i t i o n a l b o x e so f mu ffin s ? A.P2 8 C.P5 2 B. P4 0 D.P6 8

8

. Ac o n s t r u c t i o nc o mp a n yh a sj u s tc o mp l e t e dab r i d g eo v e rt h eVi s a y a na r e a .T h i st h efi r s t b r i d g et h ec o mp a n ye v e rb u i l ta n di tr e q u i r e d1 0 0we e k st oc o mp l e t e .No wh a v i n gh i r e da b r i d g ec o n s t r u c t i o nc r e wwi t hs o mee x p e r i e n c e ,t h ec o mp a n ywo u l dl i k et oc o n t i n u eb u i l d i n g b r i d g e s .Be c a u s eo f t h ei n v e s t me n t i nh e a v yma c h i n e r yn e e d e dc o n t i n u o u s l yb yt h i sc r e w, t h e c o mp a n yb e l i e v e si two u l dh a v et ob r i n gt h ea v e r a g ec o n s t r u c t i o nt i met ol e s st h a no n ey e a r ( 5 2we e k s )p e rb r i d g et oe a r nas u ffic i e n t r e t u r no ni n v e s t me n t . T h ea v e r a g ec o n s t r u c t i o nt i me wi l lf o l l o wa n8 0 %l e a r n i n gc u r v e .T ob r i n gt h ea v e r a g ec o n s t r u c t i o nt i me( o v e ra l lb r i d g e s c o n s t r u c t e d )b e l o wo n ey e a rp e rb r i d g e , t h ec r e wwo u l dh a v et ob u i l da p p r o x i ma t e l y A.2a d d i t i o n a l b r i d g e s . C.3a d d i t i o n a l b r i d g e s . B. 7a d d i t i o n a l b r i d g e s . D.8a d d i t i o n a l b r i d g e s .

9

. Mo s sPo i n tMa n u f a c t u r i n gr e c e n t l yc o mp l e t e da n ds o l da no r d e ro f5 0u n i t st h a th a dt h e f o l l o wi n gc o s t s : Di r e c t ma t e r i a l s P1 , 5 0 0 Di r e c t l a b o r( 1 , 0 0 0h o u r s@ P8 . 5 0 ) 8 , 5 0 0 V a r i a b l eo v e r h e a d( 1 , 0 0 0h o u r sa t P4 . 0 0 ) 4 , 0 0 0 F i x e do v e r h e a d 1 , 4 0 0 P1 5 , 4 0 0 * Ap p l i e do nt h eb a s i so f d i r e c t l a b o rh o u r s .

1 1

.Ka r e nCo mp a n yh a st h r e es a l e sd e p a r t me n t s .De p a r t me n t Ap r o c e s s e sa b o u t5 0p e r c e n to f s a l e s ,De p a r t me n tBa b o u t3 0p e r c e n t ,a n dDe p a r t me n tCa b o u t2 0p e r c e n t .I nt h ep a s t , De p a r t me n t sA,B,a n dCh a de r r o rr a t e so fa b o u t2p e r c e n t ,5p e r c e n t ,a n d2 . 5p e r c e n t , r e s p e c t i v e l y .Ar a n d o ma u d i to ft h es a l e sr e c o r d sy i e l d sar e c o r d i n ge r r o ro fs u ffic i e n t ma g n i t u d et od i s t o r tt h ec o mp a n y ’ sr e s u l t s . T h ep r o b a b i l i t yt h a tDe p a r t me n tAi sr e s p o n s i b l e f o rt h i se r r o ri s A.0 . 5 0 C.0 . 2 0 B.0 . 3 3 D.0 . 2 5

1 2

.Ab e v e r a g es t a n dc a ns e l le i t h e rs o f t d r i n k so rc o ff e eo na n yg i v e nd a y .I ft h es t a n ds e l l s s o f t d r i n k sa n dt h ewe a t h e ri sh o t , i t wi l l ma k eP2 , 5 0 0 ;i f t h ewe a t h e ri sc o l d , t h ep r o fi t wi l l b e P1 , 0 0 0 .I f t h es t a n ds e l l sc o ff e ea n dt h ewe a t h e ri sh o t , i t wi l l ma k eP1 , 9 0 0 ; i f t h ewe a t h e ri s c o l d , t h ep r o fi twi l l b eP2 , 0 0 0 .Th ep r o b a b i l i t yo fc o l dwe a t h e ro nag i v e nd a ya tt h i st i mei s 6 0 %.Th ee x p e c t e dp a y o ffi f t h ev e n d o rh a sp e r f e c t i n f o r ma t i o ni s A.P3 , 9 0 0 C.P2 , 2 0 0 B.P1 , 3 6 0 D.P1 , 9 6 0

716

Fi nanc i alManagement ( E.Quant i t at i veMet hods)

I ft h ec o mp a n yd e s i r e sa n8 5 %s e r v i c el e v e li ns a t i s f y i n gs a l e sd e ma n d ,wh a ts h o u l dt h e i n i t i a l b a l a n c eb ef o re a c hd a y ? A.1 9 1 C.2 3 4 B.2 2 5 D.2 5 0

1 3

. The Teeners’ Club sells fresh hot cider at Recto football games. The frequency distribution of the demand for cups of hot cider per game is presented below: Un i t s a l e sv o l u me Pr o b a b i l i t y 1 0 , 0 0 0 0 . 1 0 2 0 , 0 0 0 0 . 1 5 3 0 , 0 0 0 0 . 1 5 4 0 , 0 0 0 0 . 4 0 5 0 , 0 0 0 0 . 2 0 T h eh o tc i d e ri ss o l df o rP3 5 . 0 0ac u pa n dt h ec o s tp e rc u pi sP2 0 . 0 0 .An yu n s o l dh o t c i d e r i sd i s c a r d e db e c a u s ei t wi l l s p o i l b e f o r et h en e x t g a me . Wh a ti st h ee s t i ma t e dd e ma n df o rh o tc i d e ra tt h en e x tf o o t b a l lg a mei fad e t e r mi n i s t i c a p p r o a c hb a s e do nt h emo s t l i k e l yo u t c o mei su s e d ? A.3 4 , 5 0 0 C.1 6 , 0 0 0 B.4 0 , 0 0 0 D.5 0 , 0 0 0

Qu e s t i o nNo s . 1 7a n d1 8a r eb a s e do nt h ef o l l o wi n g: Sa mp a g u i t aCo mp a n yma k e sc o r s a g e st h a ti ts e l l st h r o u g hs a l e s p e o p l eo nt h es t r e e t s .Ea c h s e l l sf o rP2a n dh a sv a r i a b l ep r o d u c t i o nc o s t so fP0 . 8 0 . Th es a l e s p e o p l er e c e i v eaP0 . 5 0 c o mmi s s i o no ne a c hc o r s a g et h e ys e l l ,a n dt h ec o mp a n ymu s ts p e n dP0 . 0 5t og e tr i do fe a c h u n s o l dc o r s a g e .T h ec o r s a g e sl a s t f o ro n l yo n ewe e ka n dc a n n o t b ec a r r i e di ni n v e n t o r y .

The manager of the firm had estimated demand per week and associated probabilities as follows: De ma n d 1 0 0 , 0 0 0 1 2 0 , 0 0 0 1 4 0 , 0 0 0 1 6 0 , 0 0 0

1 4

.Gr e e nCo .i sc o n s i d e r i n gt h es a l eo fb a n n e r si na ne x h i b i tf a i r .Gr e e nCo .c o u l dp u r c h a s e t h e s eb a n n e r sf o rP7 . 5 0e a c h .Un s o l db a n n e r swo u l db eu n r e t u r n a b l ea n dwo r t h l e s sa f t e r t h ee x h i b i t .Gr e e nwo u l dh a v et or e n tab o o t ha tt h es t a d i u mf o rP4 , 0 0 0 .Gr e e ne s t i ma t e s s a l e so f 2 , 0 0 0b a n n e r sa t P2 0 . 0 0e a c h .I f Gr e e n ’ sp r e d i c t i o np r o v e st ob ei n c o r r e c t a n do n l y 1 , 5 0 0b a n n e r swe r es o l d , t h ec o s t o f t h i sp r e d i c t i o ne r r o rwo u l db e : A.P 6 , 2 5 0 C.P 4 , 7 5 0 B.P1 0 , 0 0 0 D.P3 , 7 5 0

1 6

.Th eo p t i ma l we e k l yp r o d u c t i o no f t h ec o r s a g ei s A.1 2 0 , 0 0 0 C.1 3 4 , 0 0 0 B.1 4 0 , 0 0 0 D.1 4 5 , 0 0 0

1 7

.Th ev a l u eo f p e r f e c t i n f o r ma t i o ni s A.P1 4 , 4 0 0 B.P1 6 , 0 0 0

1 5

. The manager of Batanes Company has developed the following probability distribution of dairy sales of a highly perishable product. The company restocks the product each morning: X( Un i t sSo l d 1 5 0 1 7 5 2 0 0 2 2 5 2 5 0 2 7 5

Pr o b a b i l i t y 0 . 2 0 0 . 2 0 0 . 3 0 0 . 3 0

C.P2 3 , 8 0 0 D.P2 2 , 1 0 0

Qu e s t i o nNo s . 2 1t hr o ug h2 4r eb a s e dont hef ol l o wi n gi n f o r ma t i o n:

Glassco, Inc. has two products, a frozen dessert and ready-to-bake breakfast rolls, ready for introduction. However, plant capacity is limited, and only one product can be introduced at present. Therefore, Glassco has conducted a market study, at a cost of P26,000, to determine which product will be more profitable. The results of the study show the following sales patterns.

P( Sa l e s= X) 0 . 2 0 0 . 4 0 0 . 1 5 0 . 1 0 0 . 1 0 0 . 0 5

Sa l e so f De s s e r t sa t P1 . 8 0p e ru n i t V o l u me Pr o b a b i l i t y 717

Sa l e so f Ro l l sa t P1 . 2 0p e ru n i t V o l u me Pr o b a b i l i t y

Fi nanc i alManagement ( E.Quant i t at i veMet hods)

2 5 0 , 0 0 0 3 0 0 , 0 0 0 3 5 0 , 0 0 0 4 0 0 , 0 0 0

. 3 0 . 4 0 . 2 0 . 1 0

2 0 0 , 0 0 0 2 5 0 , 0 0 0 3 0 0 , 0 0 0 3 5 0 , 0 0 0

De c i s i o nT r e e 2 2 . Awi n ema k e rmu s td e c i d ewh e t h e rt oh a r v e s tg r a p e sn o wo ri nf o u rwe e k s .Ha r v e s t i n gn o w wi l l y i e l d1 0 0 , 0 0 0b o t t l e so f wi n en e t t i n gP2p e rb o t t l e .I f t h ewi n ema k e rwa i t sa n dt h ewe a t h e r t u r n sc o l d( p r o b a b i l i t y0 . 2 ) ,t h ey i e l dwi l l b ec u ti nh a l fb u tn e tP3 p e rb o t t l e .I ft h ewe a t h e r d o e sn o t t u r nc o l d , t h ey i e l dwi l l d e p e n do nr a i n .Wi t hr a i n( p r o b a b i l i t y0 . 5 ) , af u l l y i e l dn e t t i n g P4p e rb o t t l ewi l l r e s u l t .Wi t h o u tr a i n( p r o b a b i l i t y0 . 5 ) ,t h e r ewi l l s t i l lb eaf u l l1 0 0 , 0 0 0 b o t t l e y i e l d , b u t t h en e t wi l l b eo n l yP3p e rb o t t l e . T h eo p t i ma l e x p e c t e dv a l u ei s A.P2 0 0 , 0 0 0 C.P3 5 0 , 0 0 0 B. P3 1 0 , 0 0 0 D.P4 0 0 , 0 0 0

. 2 0 . 5 0 . 2 0 . 1 0

The costs associated with the two products have been estimated by Glassco’s cost accounting department and are shown below: I n g r e d i e n t sp e ru n i t Di r e c t l a b o rp e ru n i t V a r i a b l eo v e r h e a dp e ru n i t Pr o d u c t i o nt o o l i n g * Ad v e r t i s i n g

De s s e r t 0 . 4 0 0 . 3 5 0 . 4 0 4 8 , 0 0 0 . 0 0 3 0 , 0 0 0 . 0 0

P

Ro l l s P 0 . 2 5 0 . 3 0 0 . 2 0 2 5 , 0 0 0 . 0 0 2 0 , 0 0 0 . 0 0

T he o r yo fCon s t r a i n t s 2 3

. Happy Holidays produces three products: X, Y, and Z. Two machines are used to produce the products. The contribution margins, sales demands, and time on each machine (in minutes) is as foll...