Determine the maximum utility if the production function is P = 20 – x2 + 10x – 2y2 + 5y, the prices of inputs x and y are 2 and 1, respectively, and the unit price of product P is 5.
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unconstrained optimization application exercises
Determine the maximum utility if the production function is P = 20 – x2 + 10x – 2y2 + 5y, the prices of inputs x and y are 2 and 1, respectively, and the unit price of product P is 5.
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- Q1 (b) – each graph needs to be approximately half page in size. All the axis need to be labeled. The TU values need to be scaled as follows: 10, 20, 30, 40, 50, 60 – with 2 cm gaps. The MU values need to be scaled as follows: -5, 0, 5, 10, 15 – with 2 cm gaps. b) Using the values from the above table, “Plot” (on separate graphs) i) Total UtilityI have two utility equations U= x^2 + y^2 U = x + ay Please draw the IC curves for each of them. And also, find the cost function associated with them and detailed steps. P.s The cost function for U= x+ay is u.min((p(x),p(y)/a)), but do not know how to get iSolve the following Multivariate Optimization: Utility Function
- Ms. Beauty's incremental benefit per day from drinking soda is given in the following scenarios. She values the first soda she drinks at P120, the second at P115, the marginal benefit for 3 soda is P95 and finally the marginal benefit for 4 soda is P60. If the price of soda is P100, the optimal number of soda that Ms. Beauty should drink is: *Find the optimal solution for the following problem. Minimize C = 4x + 12y subject to 3x + 5y ≥ 12 6x + 2y ≥ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the minimum value of the objective function?Production Function: q=32n+2nl+16l n is the size of net l is the hours of labor employed Total Cost: C=14+2n2+4l2 The price of fish is $2 per unit of fish What is the first order condition with respect to l?
- Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of candy is at least equal to the total number of cake and bread. What is the correct linear constraint to show this? Group of answer choices z – x – y ≥ 0 x – 2y – z ≥ 0 y – x – z ≥ 0 x – y – z ≥ 0Maria can purchase shirts for $22.00 each. She considers the benefit of one shirt to be $40.00, but with each additional shirt she purchases the benefit decreases by $5. According to the Principle of Optimization at the Margin, Maria will purchase... shirts. (Enter your response as a whole number.)No written by hand solution Additional units of a variable input are added to a fixed input. Total output rises from 0 units to 100 units to 190 units to 270 units to 310 units. This represents ______. a. diminishing marginal utility b. diminishing marginal returns. c. increasing MPP of the variable input d. total output rising at a constant rate
- True/False Marginal utility is 0 for the Consumption of the very first unit.The activity driver for the packing activity is the number of packing hours. Product A uses 50 packing hours and Product B uses 150 packing hours. Calculate the consumption ratios for each product. Group of answer choices 0.3; 0.7 1; 3 0.25; 0.75 0.215; 0.785Find the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x + 5y ≤ 12 6x + 2y ≤ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? (Round your answer to 3 decimal places.) What is the maximum value of the objective function? (Round your answer to 3 decimal places.)