Mathematics

(a)As the quality control engineer of a bolt production company, you are asked to perform daily checking on the bolt produced by your company in order to ensure the quality is up to the customer’s requirement. Figure Q1a shows the bolt produced by your company. Note that the bolt is either acceptable (A) or non-acceptable due to having defect structure (D). Suppose that four bolts were randomly picked by you and let X = numbers of defective bolt found. Assess all the possible outcomes, probability, and percentage of probability for the random variable X mentioned in the question. Then, compute the probability that you will encounter at least two bolts is defective.

(b) A radar unit is used to measure speeds of cars on a highway. It is known that the speeds are normally distributed and having a mean of 100 km/hr and a standard deviation of 18 km/hr. Compute the probability that a randomly monitored car on the highway has a speed ranging between 95 km/hr …

(a)As the quality control engineer of a bolt production company, you are asked to perform daily checking on the bolt produced by your company in order to ensure the quality is up to the customer’s requirement. Figure Q1a shows the bolt produced by your company. Note that the bolt is either acceptable (A) or non-acceptable due to having defect structure (D). Suppose that four bolts were randomly picked by you and let X = numbers of defective bolt found. Assess all the possible outcomes, probability, and percentage of probability for the random variable X mentioned in the question. Then, compute the probability that you will encounter at least two bolts is defective. Read More »

Consider the following problem: Minimize Z= 5×1 + 722 subject to 201 + 3×2 > 147 3×1 + 4×2 > 210 i + 22 > 63 x1 > 0, x2 > 0. (1) 2) (3) (a) Let M +0. Let Z = -2. Let e; and a; be the excess and artificial variables for the constraint i (i = 1,2,3). Construct the initial big-M simplex tableau in canonical form. (b) Identify X5,X, C, A, b and Zo of the matrix equation for the initial simplex tableau. (c) A basis for the problem is given by 12 IB= ei 21 Construct the corresponding big-M simplex tableau by the fundamental insight. (d) Find the optimal solution for (x1, x2) and the associated optimal value for Z. (Note: You may use either tabular form or matrix form of the big-M simplex method.)

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A homicide victim is found at 6: 00 PM in an office building that is maintained at 72 degree F. When the victim was found, his body temperature was at 85 degree F. Three hours later at 9: 00 PM, his body temperature was recorded at 78 degree F. Assume the temperature of the body at the time of death is the normal human body temperature of98.6 degree F. The governing equation for the temperature theta of the body is d theta/dt = – k(theta – theta_) where, theta = temperature of the body, F, theta_ = ambient temperature, F, t = time, hours, k constant based on thermal properties of the body and air. Estimate the time of death.

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