MATH Berkeley City College Sides of an Open Top Rectangular Box Questions

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Guhttlornem

Mathematics

Berkeley City College

MATH

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Hi I need help on a practice quiz on Unconstrained Optimization and Constrained Optimization/Lagrange Multipliers. I will attach example problems/videos on how to solve the problems before the practice test. I need all work to be shown and answers to be boxed.

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Find the critical point of the function f(x, y) = 6 + 7x – 2x2 + 8y + 7y2 8 14 This critical point is a: Saddle Question Help: D Video Suppose that f(x, y) = 4x4 + 4y4 – 2xy Then the minimum value is - 8 Question Help: Video Find and classify the critical points of z = (22 – 6x) (y2 – 5y) Local maximums at: (3,3) Local minimums at: DNE Saddle points at: (0,0),(0,5),(6,0),(6,5) For each of the fields above, enter an ordered pair (x, y) (or a comma-separated list of ordered pairs) where the max/min/saddle occurs. If there are none enter DNE. Question Help: D Video A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the first model made, and let y represent the number (in millions) of the second model made. The company's revenue can be modeled by the equation R(x, y) 90x + 1807 – 2x2 – 4y2 – xy Find the marginal revenue equations Rz(x, y) = 90 – 4x – y Ry(x,y) = 180 – 8y - 2 We can achieve maximum revenue when both partial derivatives are equal to zero. Set Rx 0 and Ry O and solve as a system of equations to the find the production levels that will maximize revenue. Revenue will be maximized when: X = 17.4194 y = 20.3226 O- Question Help: D Video An open-top rectangular box is being constructed to hold a volume of 350 in”. The base of the box is made from a material costing 6 cents/in2. The front of the box must be decorated, and will cost 9 cents/in2. The remainder of the sides will cost 4 cents/in?. Find the dimensions that will minimize the cost of constructing this box. Front width: 6.59758 in. Depth: 10.72106 om in. Height: | 4.94818 in. Question Help: Video Find the maximum and minimum values of the function f(x, y) = exy subject to x3 + y2 = 54 Please show your answers to at least 4 decimal places. Enter DNE if the value does not exist. Maximum value: 8103.0839 0 Minimum value: DNE Ꮕ Question Help: D Video Suppose a Cobb-Douglas Production function is given by the following: P(L,K) = 700.75 0.25 where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $400 and each unit of capital costs $800. Further suppose a total of $192,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint? Units of labor, L Units of capital, K B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production units Question Help: D Video Submit Question Suppose a Cobb-Douglas Production function is given by the function: P(L, K). = 2440.8 K0.2 Furthemore, the cost function for a facility is given by the function:C(L, K) = 300L + 500K Suppose the monthly production goal of this facility is to produce 12,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = (Show your answer is exactly 1 decimal place) Units of Capital K = (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 12,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 12,000 units is $ Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate to get a relationship between L and K. 3. Round your values for L and K to one decimal place (tenths). Question Help: D Video nswered Question 1 > ssment" ONLY if Proctorio and Camera line 'Labs Desmos Scientific Calculator Desmos Graphing Calculator 17 ach Find the critical point of the function f(2, y) = 2 + 6x + 7x2 - 5y - 4y? This critical point is a v Select an answer Saddle Maximum Submit Question Minimum WS w aut 3331 2 || Proctorio is sharing your 18 200 answered Question 2 Online ng/Labs > Assessment" ONLY if Proctorio and Camera tor Suppose that f(x, y) = x4 + y4 - 2xy Then the minimum value is coach Submit Question 1993 1 Proctorio is sharing your sc 18 O Question 3 1 > Proctorio and Camera are active An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is made from a material costing 7 cents/in?. The front of the box must be decorated, and will cost 10 cents/in? The remainder of the sides will cost 2 cents/in?. Find the dimensions that will minimize the cost of constructing this box. Front width: in. Depth: in. Height: in. Submit Question 1 Proctorio is sharing your screen. 18 BO Question 4 Proctorio and Camera are activ Find the maximum and minimum values of the function f($, y) = efy subject to 2 + y = 54. Hint: one of these values exists, and the other one doesn't exist. Maximum value: Please show your answers to at least 2 decimal places. Enter DNE if the value does not exist. Minimum value: Submit Question Proctorio is sharing your screen. * $ 18. Question 5 start Assessment" ONLY if Proctorio and Camera are active. Q9P1 0/5 answered Suppose a Cobb-Douglas Production function is given by the function: P(L,K) = 24LSKI Furthemore, the cost function for a facility is given by the function:C(L,K) = 100L + 500K Suppose the monthly production goal of this facility is to produce 5,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L. (Show your answer is exactly 1 decimal place) Units of Capital K (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 5,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 5,000 units is $ Submit Question Hide Stop sharing Proctorio is sharing your screen. 18.
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