Max Z x, +8x, Subject to (1) * +3x, 56 2x, + x, 8 X, X, 20 %3D
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- At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 50 + z + u and x − y + z − u = 58. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo GoogleAt the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 12 x + y = 44 + z + u and x − y + z − u = 36. How large was the audience of each of the four companies at the end of that year? Microsoft million Time Warner million Yahoo million Google millionA diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and atleast 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units ofVit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit.A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and eachbrand Y capsule costs P9.00, how many capsules should the patient take each day tominimize the costs? Solve using graphical method. Show complete solution.Required:1. Formulate the following:a. Decision variablesb. Objective functionc. Constraints2. Graph3. Identify feasible region.4. Solve for the value of X and Y at each point.5. Decision.
- A diabetic patient needs at least 30 units of vitamin A, at least 45 of vitamin C, andat least 30 of vitamin E each day. Each brand X multivitamin capsule contains 4units of A, 6 of C, and 2 of E; each brand Y capsule contains 5 units of A, 3 of C,and 5 of E. If each brand X capsule costs ₱ 6 and each brand Y costs ₱ 9, howmany capsules should the patient take each day in order to minimize the cost?A diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?Consider a labor market for men and women with two types of workers in each group, high ability (H types), and low ability (L types). H types among men and women have a productivity of 70 and L types among men and women have a productivity of 30. Among women 2/3rds are H types, and 1/3rd are L types, and among men ½ are H types, and ½ L types. Suppose affirmative action for women reduces the cost of college for all women to 10. What happens to the average wage gaps between men and women? Recall that employers know the shares of H and L types, but cannot observe individual types. ● Women on average make around 12% more than men. ● Women on average will make 40% more than men. ● Men will make 40% more than women. ● Women on average make 2/3rds more than men.
- A chemical manufacturer wants to lease a fleet of 22 railroad tank cars with a combined carrying capacity of 414,000 gallons. Tank cars with three different carrying capacities are available: 9,000 gallons, 18,000 gallons, and 36,000 gallons. Letting t = number of 36,000 railroad tank cars in the fleet, 2t -2 9,000 gallon railroad tank cars, and -3t+24 18,000-gallon railroad tank cars will be in the fleet for a certain range of t. The cost of leasing 9,000-gallon tank car is $250 per month, 18,000-gallon tank car is $750 per month, and a 36,000-gallon tank car is $1350 per month. Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leading costThe parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. a. What is the probability that a part that passes quality control inspection was produced by Machine Y? Enter your answer in decimal form and round to four decimal places if rounding is necessary. Blank 1. Calculate the answer by read surrounding text.b. What is the probability that a part doesn't pass quality control inspection? Enter your answer in decimal form and round to four decimal places if rounding is…The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. a. What is the probability that a part that passes quality control inspection was produced by Machine Y? Enter your answer in decimal form and round to four decimal places if rounding is necessary.
- The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. d. What is the probability that a part is produced by Machine X and doesn't pass quality control inspection? Enter your answer in decimal form and round to four decimal places if rounding is necessary.The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. c. What is the probability that a part passes quality control inspection, given that it was produced by machine Z? Enter your answer in decimal form and round to four decimal places if rounding is necessary.The parts produced at a certain factory are produced by three machines: Machine X, Machine Y, and Machine Z. 2% of the parts produced by Machine X don't pass quality control inspection, 2% of the parts produced by Machine Y don't pass quality control inspection, and 4% of the parts produced by Machine Z don't pass quality control inspection. Machine X produces 24% of the factory's total output, Machine Y produces 35% of the factory's total output, and Machine Z produces 41% of the factory's total output. Use this information to answer the following questions. b. What is the probability that a part doesn't pass quality control inspection? Enter your answer in decimal form and round to four decimal places if rounding is necessary.
