Use the method of Lagrange multipliers to determine the critical points of f(x, y) = 4x² + 2 y² +3 subject to the constraint x+ 2y = 9. Use the method of Lagrange multipliers to determine the critical points of f(x, y) = x + 2y subject to the constraint xy = 8.
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- constraint optimization 1. a. use the substitution method. given the production function, Q=5k+3L+2KL, choose the input to maximized output subject to the constraint that the planned expanditure on input is 140 dollars. each unit of labour cost 4 dollars and each unit of capital cost 20 b. use the langrange multiplier given Z=4x2+3xy+6y2, subject to the constraint x+y=56Is the function v(x1,x2)=x21x32 a monotonic transformation of u(x1,x2) ? Select one: a. No b. YesDefine the conditions for a weakly quasi-concave Cobb-Douglas Function
- Sales are the function of advertising in The Dawn and Diva Magazine (X, Y). S = XY2 If the price of advertising in The Dawn and Diva Magazine is Rs.5 and Rs.10 respectively. The total budget for advertising is Rs.105. For maximizing the sales of Dawn and Diva Magazine find out the best combination of advertisements in newspapers and magazines by using the Lagrangian multiplier. please provide a complete solution with all the steps including formulas and proper workingRobinson Crusoe has exactly 12 hours per day to spend gathering coconuts ( C) or catching fish (F). Let tp denote the time (in hours) spent catching fish and tc the time (in hours) spent gathering coconuts per day. Robinson can catch 3 fish per hour or he can gather 6 coconuts per hour; his "production technology" can thus be described by: F = 3tp and C = 6tc. Robinson's utility function is U(F,C) = FC where F is his consumption of fish and C is his consumption of coconuts. 1. (a) Write down Robinson's time constraint and hence find an equation for his Production Possibility Frontier (PPF). (b) Find the number of fish Robinson will catch per day and the number of coconuts he will gather per day.Maximize the function f(x)= x^2/5 (10-2x)^1/3 a. Give maximization problem. b. Give first order conditions for the maximization problem. c. Find the solution to this maximization problem.
- why is there no inclusion of the parameter z in the solutions and the budget constraint?Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars. Estimated Sales Volume = 48.06 + 0.53 (Advertising Expenditures) If the company has a target sales volume of $100,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.Tim is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $4.00, and a bowl of salad costs $5.00. Let ♬ be the amount in dollars that Tim spends on pizza and salad. If Tim buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Tim has $40.00 to spend on pizza and salad; that is, E = $40.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Tim can purchase with $40.00, when the number of pizza slices he purchases is 0. Budget Pizza (Dollars) (Slices) 40.00 0 40.00 5 40.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Tim can purchase with a budget of $40.00. SALAD (Bowis) 14…
- In the 1980s, President Reagan based his tax and spending policies õñ supply side economics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let t denote the tax rate, w the real wage rate, and n the labor supply. The tax revenue is T = wnT where wn is labor income, which is the tax base. For convenience, assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rateT increases, workers substitute toward leisure and away from consumption. Hence as 7 rises, wn falls and tax revenue falls for high enough tax rates. Let U, V satisfy the standard assumptions. The model is static and households are endowed with one unit of time. A…In the 1980s, President Reagan based his tax and spending policies on supply side economics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let T denote the tax rate, w the real wage rate, and n the labor supply. The tax revenue is T = wNT where wn is labor income, which is the tax base. For convenience, assume w is constant. There is no reason for this assumption to be true, but we impose it to focus on the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute toward leisure and away from consumption. Hence as T rises, wn falls and tax revenue falls for high enough tax rates. Let U,V satisfy the standard assumptions. The model is static and households are endowed with one unit of time. A…The function Q = F(p,ps,y) describes how the monthly demand, Q (measured in 100s of Widgets), for Grinch Inc. Widgets depends on the variables: • p = the price/Widget that Grinch Inc. sets (measured in $). • Ps= average price of substitutes for Grinch Inc. Widgets (measured in $). • y = average disposable income in the market for Widgets (measured in $1000s). When average disposable income in the market is $4200 and Grinch Inc.s price is $12 and the average price of substitutes is $11... ● Q = 66 •Op=-0.28 2ps = 0.52 ● Qy = 0.31 If average monthly income increases to $4400 and the average price of substitutes increases to $11.35, by approximately how much can Grinch Inc. increase their price while keeping demand for their Widgets fixed at Q = 66 ? Ο Δp = 0.87 O There is no way to estimate this from the given information.. Ο Δρ = 0.53 O Ap = 0.72