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m = 3 n = 4
Find linear equation system solution with the method of Cramer Rule
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- 2.1 Provide solution for d,e,f parts Last 3 partsA 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?
- 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 Google2. Solve using Gauss Jordan Elimination Method. Compute also for x, y and z.15. General Solution of xdy-ydx=x2exdx is
- 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) + 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 millionAt 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) + 10 x + y = 50 + z + u and x − y + z − u = 46. How large was the audience of each of the four companies at the end of that year?Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…
- a) The base chassis of a manufactured product is made up of numerous components. There can sometimes be differences in dimensions between components, requiring the partially assembled product to be sent to another department for extra fitting work because some components cannot be fitted in place. The majority of fitting problems are caused by two particular components (identified as B and F): the chances of a randomly chosen component of type B not fitting are 3.7%, and the chances of a randomly chosen component of type F not fitting are 2.8%. (i) Given that the problems with fitting these two components are independent of each other and that components are selected randomly for assembly on each base chassis, what is the probability that both components B and F will have problems fitting on a given chassis? ii) How likely is it that there will be problems fitting components B and F to a given chassis under the same assumptions? (b) (i) The probability distribution of the number of…a) The base chassis of a manufactured product is made up of numerous components. There can sometimes be differences in dimensions between components, requiring the partially assembled product to be sent to another department for extra fitting work because some components cannot be fitted in place. The majority of fitting problems are caused by two particular components (identified as B and F): the chances of a randomly chosen component of type B not fitting are 3.7%, and the chances of a randomly chosen component of type F not fitting are 2.8%. (i) Given that the problems with fitting these two components are independent of each other and that components are selected randomly for assembly on each base chassis, what is the probability that both components B and F will have problems fitting on a given chassis? ii) How likely is it that there will be problems fitting components B and F to a given chassis under the same assumptions? (b) (i) The probability distribution of the number of…Suppose 51 percent of the customers at Pizza Palooza order a square pizza, 73 percent order a soft drink, and 47 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Yes No