Question 1

Two factories “A” and “B” produce radios. Each radio produced at factory-A is defective with probability 0.05, whereas each radio produced at factory-B is defective with probability 0.1. You purchase two radios that were produced in the same factory (which is equally likely to have been either factory-A or factory-B). If the first radio that you check is defective, what is the conditional probability that the second radio is also defective? (*Note: Enter your* **answer in decimals** *rounded to* *two decimal places. For example, if your answer is “0.456” then* **enter it as “0.46”***)* Milo’s Survey Services (MSS) specializes in evaluating the reaction of customers to new products. A client has hired MSS to ascertain customer reaction to a recently launched product (Frying Pan). During meeting with the client, MSS agreed to conduct door-to-door personal interviews to obtain responses from households with children and without children. In addition, MSS agreed to conduct both “Daytime” and “Evening time” interviews. Specifically, the client’s contract called for MSS to conduct 1000 interviews under the following quota guidelines\ i. Interview at least 400 households with children\ ii. Interview at least 400 households without children\ iii. The total number of households interviewed during evening must be at least as great as the number of households interviewed during the day\ iv. At least 40% of the interviews for households with children must be conducted during the evening\ v. At least 60% of the interviews for households without children must be conducted during evening\ Because the interviews for households with children take additional interview time and because evening interviewers are paid more than daytime, the cost varies with type of interview. Based on previous surveys conducted, MSS estimates the interview costs as given in Table-1 Figure from the passage in the original paper MSS wanted to conduct the interviews so that the overall cost for conducting the survey is minimized. Given this information, answer the subquestions. How many (count of) decision variables are present in the standard form of the primal? Milo’s Survey Services (MSS) specializes in evaluating the reaction of customers to new products. A client has hired MSS to ascertain customer reaction to a recently launched product (Frying Pan). During meeting with the client, MSS agreed to conduct door-to-door personal interviews to obtain responses from households with children and without children. In addition, MSS agreed to conduct both “Daytime” and “Evening time” interviews. Specifically, the client’s contract called for MSS to conduct 1000 interviews under the following quota guidelines\ i. Interview at least 400 households with children\ ii. Interview at least 400 households without children\ iii. The total number of households interviewed during evening must be at least as great as the number of households interviewed during the day\ iv. At least 40% of the interviews for households with children must be conducted during the evening\ v. At least 60% of the interviews for households without children must be conducted during evening\ Because the interviews for households with children take additional interview time and because evening interviewers are paid more than daytime, the cost varies with type of interview. Based on previous surveys conducted, MSS estimates the interview costs as given in Table-1 Figure from the passage in the original paper MSS wanted to conduct the interviews so that the overall cost for conducting the survey is minimized. Given this information, answer the subquestions. Excluding the non-negativity constraint, how many (count of) constraints are present in the standard form of the primal?