(ii) Suppose that f(x,y) = xy. Find the maximum value for f(x,y) if x and y are constrained to sum to 4. Solve this problem by using Lagrange multiplier method.
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- The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per %3D week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume A bags of candy.Solve each of the following equations for x x+7=14 5x+4=24 12−4x=−20 Organize each of the following equations to express Pas a function of Q. QQ as a function of P PP as a function of Q Q=25−P Q=12−3P 6Q=14−2PDerive the MU function from the following TU function: ?? = 200? − 25?2 + ?3
- Come up with two variables that, in your view, are related, indicate the name of these variables as well as why these variables are related; determine which variable is the dependent variable and which one is the independent variable. Draw a line graph by hand, labeling the vertical and horizontal axis consistent with your choice of variables. The line in the line graph has to represent, what, in your view, is the relationship between the two variables. Describe your graph verbally in your post (no need to upload the graph itself). Note:- • Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. • Answer completely. • You will get up vote for sure.Population of Fish in a Lake A lake is stocked with 100 fish. Let f(1) be the number of fish after i months, and suppose that y = f(1) satisfies the differential equation y' = .0004y(1000 – y). Figure 7 shows the graph of the solu- tion to this differential equation. The graph is asymptotic to the line y = 1000, the maximum number of fish that the lake can support. How fast is the fish population growing when it reaches one-half of its maximum population? 1000 800 600 400 200 10 15 Figure 7 Growth of a fish population.Using first order conditions find the stationary values of the following (check whether they are relative maxima or minima or inflection points), assuming the domain to be the set of all real numbers.a) Y= -2X²+8x + 7b) Y= 5X² –xc) Y= 3X² +3
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