1) A Manufacturing process produces thousands of semi-conductors chips per day. On the average, 1% of these chips do not conform to the specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or non – conforming. If we let x be the random variable representing the number of non-conforming chips in the sample, then what is the probability distribution of x?why?

20. A tachometer normally refers to a(n) _______ used for speed measurement. a. load cell c. ultrasonic sensor b. capacitive proximity sensor d. small generator

6) The fill volume of soft-drink beverage bottles is an important quality characteristic. The volume is measured(approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale, a reading of zero corresponds to the correct fill height. Fifteen samples of size n = 10 have been analyzed, and the fill heights are shown in Table 6E.5. a)What control charts are more suitable to monitor the mean and variability of the process? b) Construct the control charts and set the valid control limits c) Is the process in control?

The owner of a restaurant that serves Continental-style entrées has the businessobjective of learning more about the patterns of patron demand during the Friday-to-Sunday weekend time period. Data were collected from 630 customers on the type ofentrée ordered and were organized in the following table: a) Construct a percentage summary table for the types of entrées ordered. [1mark] b) Based on the percentage summary table, construct a bar chart, a pie chart, adoughnut chart, and a Pareto chart for the types of entrées ordered. [4 marks] c) Do you prefer using a Pareto chart or a pie chart for these data? Briefly explainyour preference. [2 mark] d) What conclusions can the restaurant owner reach concerning demand fordifferent types of entrées? Briefly explain. [2 marks] Suppose that the owner of the restaurant also wants to study the demand for dessertduring the same time period. She decides that in addition to studying whether adessert was ordered, she will also study the gender of the individual and whether abeef entrée was ordered. Data were collected from the same 630 customers and areorganized in the following contingency tables: e) For each of the two contingency tables, construct contingency tables of row,column and overall total percentages. [6 marks] f) Which type of percentage (row, column, or overall total) do you think is mostinformative for each gender? For beef entrée? Briefly explain. [3 marks] g) What conclusions concerning the pattern of dessert ordering can the restaurantowner reach? Briefly explain. [2 marks]

MATH 308 - Assignment 1 1. Find necessary and sufficient conditions for the numbers s and t to make the LP problem Maximize: f(x1, x2) = x1+x2 subject to sx1+tx2 ≤ 1 x1, x2 ≥ 0 a) have an optimal solution. b) be infeasible. c) be unbounded. Prove your answers.

A company intending to produce components for a fit with guaranteed clearance / interference as given in Table Q2 (Jmin, Jmax Or Smin, Smax respectively). It has been experiencing problems when machining both holes and shafts caused by lack of process capability, see Manufacturing Methods in Table Q2. Maintaining fit characteristics transform the tolerances to suit company's capability implementing selective assembly method. 1. Determine tolerances of the mating parts based on the manufacturing methods 5. Calculate maximum and minimum interference / clearance for each group 4. Draft the tolerances, indicating the groups 3. Calculate upper and lower limit deviations for the hole and the shaft 2. Calculate the number of groups

25. For the programmed latching operation shown, which two instructions must have the same address? a. ON and OFF inputs. b. latch and unlatch outputs c. ON input and latch output d. OFF input and unlatch output

2. For the following product structure: a) Develop all the Bills of Material tables. b) Find the number of units of each of the raw materials (R's), components (C's),and subassemblies (S's) that are needed to make one unit of product P.

2) The diameter of a metal shaft used in a disk-drive unit is normally distributed with mean 0.2508 in. and standard deviation 0.0005 in. the specifications on the shaft has been established as 0.2500±0.0015 in. what fraction of the shafts produced conform to specifications?

5. A drug company sells three different formulations of vitamin complex and mineral complex. The first formulation consists entirely of vitamin complex and sells for $1 per unit. The second formulation consists of 3/4 of a unit of vitamin complex and 1/4 of a unit of mineral complex and sells for $2 per unit. The third formulation consists of 1/2 of a unit of each of the complexes and sells for $3 per unit. If the company has 100 units of vitamin complex and 75 units of mineral complex available, how many units of each formulation should the company produce as to maximize profit? Write down the corresponding LP, and solve it by using Theorem 22 and 23.