You are an Industrial Engineer at Mason Products, and as your boss, I have asked

Question

You are an Industrial Engineer at Mason Products, and as your boss, I have asked you to perform some analysis of our order history in order to plan our schedule for the next couple of months. Below is some information you will need to know to help in this analysis. . We have three sizes of jars: (1) quarter pint; (2) half pint; (3) pint . We have five types of cake: (1) chocolate; (2) vanilla; (3) yellow;(4) spice; (5) strawberry . We have four types of frosting: (1) cream cheese; (2) chocolate; (3) vanilla; (4) strawberry . We offer any combination of cake and frosting in any size. The color of label depends on cake type. Chocolate cake has a brown label; strawberry cake has a pink label; all other cakes have a white label. We use the following codes for our products: CODE DESCRIPTION ChC Chocolate Cake VC YC Vanilla cake Yellow cake SpC Spice cake StC Strawberry cake CrF Cream Cheese frosting ChF Chocolate frosting VF Vanilla frosting SF Strawberry frosting Last month's orders were as follows: ChC VC YC SpC StC CrF ChF VF SF 27 0 18 0 0 0 7 12 GRADE: /40

Explanation / Answer

= 3*5*4 = 60 types of label identifiers needed.

(ii) (a) P(YC U SC) = P(YC) + P(SC) – P(YC int SC) = 18/100 + 13/100 – 0/100 = 31/100 = 0.31

(iii) (a) P[(YC U ChF) int (ChC U ChF)] = P[(YC U ChF)*P(ChC U ChF)] = {(18+47-18)/100}*{51/100} = (47/100)*(51/100) = 0.2397

      b) P[(YC int. ChF) int (ChC int. ChF)] = P(YC int. ChF)*P (ChC int ChF) = (18/100)*(27/100) = 0.0486

     c) P[(YC int. ChF) U (ChC int. ChF)] = P[(YC int. ChF) + (ChC int. ChF)] - P[(YC int. ChF) int (ChC int. ChF)] = 18/100+ 27/100 – 0.0486 = 0.45-0.0486 = 0.4014

   d) P[(YC U ChF)| ChF)] = P[(YC U ChF) int (ChF)]/ P[(ChF)] = P[(YC int ChF) U (ChF)]/ P[(ChF)] = P[(ChF)]/ P[(ChF)] = 1.

3.Find probability that an incoming order will require vanilla frosting?

P(VF) = 18/100= 0.18

4. Find probability that an incoming order will require Chocolate cake?

P(ChC) = 31/100= 0.31.

5. P(Chocolate cake| Chocolate frosting) = P(ChC | ChF) = P(ChC int ChF)/ P(ChF) = (27/100)/(47/100) = 27/47 = 0.5744

6. P(Chocolate frosting| Chocolate cake) = P(ChF | ChC) = P(ChF int ChC)/ P(ChC)

= (27/100)/(31/100) = 0.8709.

ChC VC YC SpC StC Total CrF 0 0 0 11 1 12 ChF 27 0 18 0 2 47 VF 0 8 0 2 8 18 SF 4 12 0 0 7 23 Total 31 20 18 13 18 100

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