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- Approaching the month of Ramadan, PT Prima Sehat predicts that there will be an increase in demand for electronic goods, both TVs and microwaves. All of these electronic products have the same processing process, but have different processing times. For TV requires 4 hours of electronic processing and 2 hours of assembly. While the microwave requires 3 hours of electronic processing time and 1 hour of assembly. Of the current capacity, there is a working time for electronics as much as 240 hours, and per work time as much as 100 hours. The profit for each product is 7 (in tens of thousands) and 5 (in tens of thousands). Please use the simplex method linear programming method to solve the above caseA private investment club has $200,000 earmarked for investment in stocks. To arrive at anacceptable overall level of risk, the stocks that management is considering have been classifiedinto three categories: high risk, medium risk, and low risk. Management estimates that high-riskstocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks,6%/year. The members have decided that the investment in low-risk stocks should be equal tothe sum of the investments in the stocks of the other two categories. Determine how much theclub should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment. (Assume that all the money available for investment isinvested.)Note: Develop the linear system of equations from the above theory and solve the system byGauss Jordon Method.What is the significance of R and R2 in gression model?
- If the preceding 50% rates were each reduced to 40% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives; that is would the mortality rate decrease and, if so, what percentage of deaths among hypertensives could be prevented by the education program?You have $10,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high‐risk account has an expected (hoped‐for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high‐risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year‐end yields are as expected, what are the optimal investment amounts? a. Choose the unknowns, i.e. variables. State what they are so you know exactly what you are looking for.b. Write your OPTIMIZATION EQUATION. c. Write the constraints as a system of inequalities, usually there are several.d. Graph the system and identify the feasibility region. e. Identify the corners of the feasibility region, which will be the ordered pairs that you test in your optimization equation.f. Calculate the value of the optimization equation using each of the ordered pairs…your natural gas bill is calculated as sum of the fixed monthly cost and a rate per therm of natural gas used. given a usage of 183 therms with a bill of $116.05 for this month and a usage of 129 therms with a bill of $85.80 for last month, determind the fixed monthly cost and rate of your bill with appropriate units.
- For years, the drug Vioxx, developed andmarketed by Merck, was one of the blockbusterdrugs on the market. One of a number ofso-called Cox-2 anti-inflammatory drugs, Vioxxwas considered by many people a miracle drug foralleviating the pain from arthritis and other painfulafflictions. Vioxx was marketed heavily on television,prescribed by most physicians, and used by anestimated two million Americans.All of that changed in October 2004, when theresults of a large study were released. The study,which followed approximately 2600 subjects overa period of about 18 months, concluded that Vioxxuse over a long period of time caused a significantincrease in the risk of developing serious heartproblems. Merck almost immediately pulled Vioxxfrom the American market and doctors stoppedprescribing it. On the basis of the study, Merck facednot only public embarrassment but the prospect ofhuge financial losses.More specifically, the study had 1287 patientsuse Vioxx for an 18-month period, and it…For a particular process, originally each 200 units of product manufactured yielded 180 conforming units, 9 units that must be scrapped, and the remaining units that must be reprocessed. Each scrapped unit results in a $30 loss and each reprocessed unit requires an extra 0.30 hours of processing time. The resource time of producing the original 200 units is 30 hours. As a result of a quality improvement program that was recently introduced, for each 200 units manufactured, the process now yields 190 conforming units, 1 unit to be scrapped, and the remaining units that must be reprocessed. Calculate the scrap cost for the new process.The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). What is the residual for the United States? You can use the information on the actual y-value given in the description of the study as well as information from your response to Question 3 to calculate this. Residual for the U.S. =
- It is known that in any given year, • 90% of the people in a city move to the suburbs; • 80% of the people in the suburbs do not move to the city. Given an initial city population of 55,000 and an initial suburb population of 77,000, what are the long-term population levels of the city and the suburb?The research department at a manufacturing company has developed a new process that it believes will result in an improved product. Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market it, sales should increase by $60,000. If it is not better and they replace the old product with the new product on the market, they will lose $25,000 to competitors. If they decide not to market the new product, they will lose a total of $50,000 if it is better and just research costs of $20,000 if it is not. Answer parts a through c below. (a) Prepare a payoff matrix. Start 2 By 2 Table 1st Row 1st Column 60000 2nd Column negative 25000 2nd Row 1st Column negative 50000 2nd Column negative 20000 EndTable 60000 −25000 −50000 −20000 (Type an integer or decimal for each matrix element. Do not include the $ symbol in your answer.) (b) If…A hunger-relief organization has earmarked between $2 million and $2.5 million (inclusive) for aid to two African countries, Country A and Country B. Country A is to receive between $1 million and $1.25 million (inclusive), and Country B is to receive at least $1 million. It has been estimated that each dollar spent in Country A will yield an effective return of $0.40, whereas a dollar spent in Country B will yield an effective return of $0.80. How should the aid be allocated if the money, in millions, is to be utilized most effectively according to these criteria? Hint: If x and y denote the amount of money, in millions of dollars, to be given to Country A and Country B, respectively, then the objective function to be maximized is P = 0.4x + 0.8y.
