Suppose thatP = 4.2x² + 1.5y² - 0.1x3 -0.01y3 tonsis the production function for a product with x units of one input and y units of a second input. This function has twocritical points, the origin (0,0) and one other. The critical point with positive values of x and y yield the maximumproduction. Find the values of x and y that will maximize production.X =unitsy =unitsWhat is the maximum production? (Round your answer to the nearest whole number.)tons

Answered: Image /qna-images/answer/f21ca49f-ff54-4892-af66-4c554d038a13.jpg

Answered: Suppose that P = 4.2x² + 1.5y² - 0.1x3…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output will be maximum?
Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where x is the cost per pound for material and y is the cost per hour for labor. (a) If material costs are held constant, at what rate will the total cost increase for each $1-per-hour increase in labor? (b) If the labor costs are held constant, at what rate will the total cost increase for each increase of $1 in material cost?
A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x<200: fixed costs, $245; unit production cost, $15 per vest; equipment maintenance and repairs, 0.05x2 dollars. So, the cost of manufacturing x vests in one given day is given by C(x)=0.05x2+15x+245, where 0<x<200. (A) What is the average cost C(x) per vest if x vests are produced in one day? (B) Find the critical numbers of C(x), the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema. Do not graph
A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x<150: fixed costs, $500; unit production cost, $25 per vest; equipment maintenance and repairs, 0.05x2 dollars. So, the cost of manufacturing x vests in one given day is given by C(x)=0.05x2+25x+500,where 0<x<150. a.) What is the average cost C(x) per vest if x vests are produced in one day? b.) Find the critical numbers of C(x), the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema.
A firm has two plants that produce identical output. The costs functions are C1=10q-4q^2+q^3 MC1 = 10 - 8q + 3q^2 and C2 = 10q - 2q^2 + q^3 MC2 = 10 - 4q + 3q^2 a. At what output levels does the average cost curve of each plant reach its minimum? b. If the firm wants to produce four units of output, how much should it produce in each plant?
A 1125 ft3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top flush with the ground to catch runoff water. The costs associated with the tank involve not only the material from which the tank is made but also an excavation charge proportional to the product xy. a. If the total cost is c = 5(x2 + 4xy) + 10xy, what values of x and y will minimize it? b. Give a possible scenario for the cost function in part (a).
The company wishes to produce both products, but not at equal portions. 60% X’s and 40% Y’s is desired for production. At the indicated percentages, what is the daily capacity of this company? Hint 1: find the weighted unit load based on the given portions and apply that in the effective capacity formula. Hint 2: It will be a mistake to allocate 60% of the available time to produce X. Rather, apply hint 1 to make sure the resulting production will be 60% from X units and 40% from Y’s.
Mr Banda is consuming products A and B optimally and deriving total utility of 10 utiles. When his budget is increased from K80 to K81, his utility increases from 10 utiles to 10.1 utiles. a) What is the marginal utility of X at the optimum when the price of X is K20? b) What is the price of Y when the marginal utility of Y is 4 utiles? c) Compute the Lagrange multiplier d) What is the utility when the budget is reduced from K80 to K79?
Suppose that a company's average cost is A(x)=1.7x+7. Step 2 of 2: Determine the marginal cost.
The Cobb-Douglas production function for a particular product is N(x,y)=40x^0.6 y^0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x,y) units of a product. Each unit of labor costs $60 and each unit of capital costs $120 If $300,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production Production will be maximized when using _ units of labor and _ units of capital
Nelison Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb. The estimated demand for the cookies is 1,000,000 1-lb containers per year. The setup cost for each production run is $500, and the manufacturing cost is $0.50 for each container of cookies. The cost of storing each container of cookies over the year is $0.40. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilson produce per production run in order to minimize the production cost? C(x)=500,000,000/x + 0.2x + 500,000. Then minimize the function C on the interval (0,1,000,000).
A small computer manufacturing company forecasts the demand over the next n months to be di i = 1 2n. In any month it can produce r units, using regular production, at a cost of b dollars per unit. By using overtime, it can produce additional units at c dollars per unit, where c>b. The firm can store units from month to month at a cost of s dollars per unit per month. Formulate the problem of determining the production schedule that minimizes cost.

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