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CAS EXPERIMENT. Steepest Descent. (a) Write a program for the method.
(b) Apply your program to
c) Apply your program to
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Advanced Engineering Mathematics
- Suppose that in a certain year, the Pioneer fund was expected to yield 6%, while the BlackRock fund was expected to yield 6%. You would like to invest a total of up to $80,000 and earn at least $4,200 in interest in the coming year (based on the given yields). Draw the feasible region that shows how much money you can invest in each fund. (Place MHI on the x-axis and BKK on the y-axis.) Find the corner points of the regionarrow_forwardMutual Funds Suppose that in a certain year, the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield 4%, and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield 8%. You would like to invest a total of up to $50,000 and earn at least $2500 in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). (Place ZTR on the x-axis and MSP on the y-axis.) The x y-coordinate plane is given. There are 2 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (0, 50000), passes through the approximate point (38000, 13000) crossing the second line, crosses the x-axis at x = 50000, and exits the window in the fourth quadrant. The second line enters the window in the second quadrant, goes down and right, passes through the approximate point (0, 31000), passes through…arrow_forwardPlease do not give solution in image format thanku For a certian group, aggregated claims are uniformly distributed over (0, 10). Insurer A proposes stop-loss coverage with a deductible of 6 for a premium equal to the expected stop-loss claims. Insurer B proposes group coverage with a premium of 7 and a dividend (a premium refund) equal to the excess, if any, of 7k over claims. Calculate k such that the expected cost to the group is equal under both proposals.arrow_forward
- In regression theory, Summation(Yi-Y^) is a. Minimum/non-negative b. Zero c. One ď. Maximumarrow_forward(a) State a necessary and sufficient condition for the convergence of the Jacobi andGauss-Seidel (GS) methods.(b) Use the previous part condition to show whether the GS method converges ordiverges to the solution of the systemx + 2y = 3,3x + (0.77)y = 4.(c) Determine x(1) by applying one iteration of the GS method with x(0) = 0.arrow_forwardSolve Nonlinear Equation: Using the Fixed Point Methodx=(exp(x))/3use the following initial values to startcalculations: x= -0.1, 0.5, 0.6, 0.8, 1.0, 1.2, 1.5, 1.6 and 2.0. Interpret results by determining at whatcases the solution converges and when it diverges. Also determine whether the convergence is oscillating or not.arrow_forward
- I need help whith a homework problem, the math lab at my school is closed. For number 15, why does part a converge? I understand the part b, but do not understand anything about part a converging. Please help.arrow_forwardSolve Nonlinear Equation: Using Newton Raphson's Method(see image)use the following initial values to startcalculations: x= -0.1, 0.5, 0.6, 0.8, 1.0, 1.2, 1.5, 1.6 and 2.0. Interpret results by determining at whatcases the solution converges and when it diverges. Also determine whether the convergence is oscillating or not. Thanks in advicearrow_forwardSeries Discount This is a continuation of Exercise 11. Sometimes manufacturers give more than one discount instead of a single trade discount for example, in trading with large-volume retailers. Such a series discount is quoted as a sequence of discounts, taken one after another. Suppose a manufacturer normally gives a trade discount of 45%, but it has too much of the item in inventory and so wants to sell more. In this case the manufacturer may give all retailers another discount of 15% and may perhaps extend yet another discount of 10% to a specific retailer it wants to land as a client. In this example, the series discount would be 45%, 15%, 10%, calculated one after another, like this: For an item with a suggested retail price of 100.00, applying the first discount gives 100.00-45%100.00=55.00 dollars. The second discount of 15% is applied to the 55.00 as follows: 55.00-15%55.00=46.75 dollars. Now, the third discount gives the final cost price of 46.75-10%46.75=42.08 dollars. a. Suppose an item has a suggested retail price of 80.00 and the manufacturer is giving a series discount of 25% and 10%. What is the resulting cost price? b. Suppose an item has suggested retail price of 100.00 and the manufacturer is giving a series discount of 35%, 10%, 5%. What is the resulting cost price? c. What single trade discount would give the same cost price as a series of 35%, 10%, 5%? Note: The answer is not 50% d. Explain why we could have calculated the same answer as in part b by multiplying 100.000.650.900.95. In this case, what would the 0.65, 0.90, and 0.95 represent? Trade Discount Often retailers sell merchandise at a suggested retail price determined by the manufacturer. The trade discount is the percentage discount given to the retailer by the manufacturer. The resulting price is the retailers net cost and so is called the cost price. For example, if the suggested retail price is 100.00 and the trade discount is 45%, then the cost price is 100.00-45%100=55.00 dollars. a. If an item has a suggested retail price of 9.99 and the trade discount is 40%, what is the retailers cost price? b. If item has a cost price of 37.00 and a suggested retail price of 65.00, what trade discount was used?arrow_forward
- Areas of Curved Regions The Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of f(x)=x2, above the x-axis, between x=0 and x=1. If we choose a point in the square at random, the probability that it lies under the graph of f(x)=x2 is the area under the graph divided by the area of the square. So if we randomly select a large number of point in the square, we have numberofhitsunderthegraphnumberofhitsinthesquareareaundergraphareaofsquare Modify the program from Problem 5 to carry out this Monte Carlo simulation and approximate the required area.arrow_forwardA couple wants to invest up to $45,000. A Roth IA has a return close to 7% after one year and a CD has a rate of 4% after one year. Since a Roth IRA is riskier, they want to invest no more than $5000 in that account and at least $20,000 in a CD. How much should the couple invest in each account to maximize their return? What would the maximum return be after one year?arrow_forward1) Find intervals of increase and decrease 2) Find intervals of concavity 3) Find local maximums and minimums 4) Find inflection pointsarrow_forward
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