Question

Consider the design problem of the omicron company. They manufacture home gardening equipment. Because of the seasonal nature of their product line they build up a large inventory before their season begins. They have no way to check and alter their design decisions. (The same effect holds true for Christmas items such as toys and style goods) Omicron is restyling their plastic tubing used for garden hoses. The design alternatives that they are considering utilize the same facilities as their present product and therefore the problem of limited resources can be neglected. The question that omicron wishes to resolve is whether to make the plastic hose green, red, or yellow. These are strategies S1, S2, S3 respectively and in addition a fourth strategy make 50% red and 50% green is specified and called S4. (Ofcourse many combinations of all colors would be possible and could be easily handled by our methods.) The decision as to the best strategy is strongly influenced by an uncontrollable factor, viz., what color will be in style in the coming year. Estimates are prepared and the data are assembled as follows: Matrix of estimated sales volume (in Feet) N1 N2 N3 50,000 Green S1 100,000 50,000 50,000 50,000 150,000 Red S2 100,000 40,000 Yellow S3 30,000 Green & Red S4 125,000 125,000 75,000 Where, N1 is the state of natue, red is in style; N2 describes the fact that green is in style, and N3 stands for the condition that neither red nor green is in style. The hose sells for 15 cents a foot no matter what color is used. However, the per foot cost of each strategic alternative is different. It is 5 cents for S1, 4 cents for S2, 5 cents for S3, and 8 cents for S4. Applying the formula: Profit Sales volume (price per unit - cost per unit) Complete the following: Make up a profit matrix a. b. Map profit vs a chart Show the switch points C. d. Advise on selections based on maximax and maximin criteria Determine the best choice for a-0.6 both graphically and by equations e.

Answer 1

A6Swer- a) Profit matrix is as follow martrix of Estimated Sales volume (io feet Cost N 3 N2 0.OS SO,000 100 000 S0,000 GYeen S2 $0.04 So, 000 Red 00 000 50,000 S2 0.os Neilouw 30.000 0.08 15,0O0 Grreen Red S4 125,boD 75i000 Profit matxix N3 NI 7N GYeen S,000 So00 O00'a Red S1 Soo 11, 0o o StSoo Yello IS DOO u,000 GreenfRe Sy 8,750 5,2 So 2750 Profit is Calc ulated b Re given forenula , iie Profitz Sales volume CPyice Per-feet -Cost Per feet) vs alpha chant, need to Re alpha repr- b) for mating Proftt Probability of occurrence of e esent what . s 8t proba bilip alpha, what i^ IRe N1 Or N2 OYN3 And giuen oHRen outcome. ARis information is vegtuived below uSing wo-way 1abie tch Poiot e [C alculated

Seps to Crating tuoo-ua table me follooing : Calculate expected valu e Fn - sumpRODUCT Ca:E , Ses Сорy o Fi:FIY Co mpute Evman, Flb-max (FIIFN appropriate Styateg ,F1n INDE Determine (FIbFl),) MATCH (en Struct a blank table 2:t13 formala in 12 - Fi - Emt en values fn Re ffrst Yow 12:T2 and in Re firsi Column 13:13 o to Select 12: T13 > Data what -f onalySis >Data Table Row input cell: ci column in put ell matri of eStimated Salas volume(infeet) N2 N3 Co SH Green So,oco bo boo Red So,000 So.ooo Yelloco S2 30,000 uo, 000 0.08 25/0D0 GreenRed S TS,000 125,000 Pro bability O50 O'20 €x pected Profit matrix Value N2 NI 6500 5,000 5.060 S $10.000 Green 1,boo 6600 S,500 $5, S00 Red 200 S3 ЧеПоо 3 000 4,000 5,230 Greend Red $8,750 Sy $8, 750 ,0oo

Probability Ni) o Q 0130 O220 S3 O 00 S2 Si S3 S3 S2 S2 S Si S14 S1 $3 S1 S3 S3S2 S3 O0 S3 Sy Sy S3 S2 S3 S3 O 20 S) Sy S3 S2 S3 Sy O30 S4 Sy S4 S2 Su Su Sy Sy Sy Sy S3 S2 S2 S3 Su Su Su S S2 S2 O 60 82 SSyS Sy S2 O.20 S2 S2 Si SSi Sy Sy Sy 0 80 SL Sy S2 S2 S4 S2 S2 Sy Sy S2 S2 SL SL S4 S2 S2 S2 S2 Sy S4 Sy Sy &2 CA