The production function of the company has the form: Q(x, y) = 5 x y. The price of a unit of resource X is 10 rubles, and the price of a unit of resource Y is 20 rubles. The company has funds in the amount of 40 thousand rubles. Determine the maximum possible production volume.
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- The profit of a company, in dollars, is the difference between the company's revenue and cost. The cost, C(x), and revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors. C(x) = 2500 + 60x R(x) = 800x - x? a) Determine the maximum profit of the company. The maximum profit of the company is b) Determine the number of items that must be produced and sold to obtain the maximum profit. The number of items that must be produced and sold to obtain the maximum profit isThe profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.production function is Q = An orange grower has discovered a process for producing oranges that requires two inputs. The min{2x1, x2}, where x₁ and x2 are the amounts of inputs 1 and 2 that he uses. The prices of these two inputs are w₁ = 5 and w₂ = = 2, respectively. The minimum cost of producing 140 units is (a) $980 (b) $630 (c) $1400 (d) $280 (e) $700
- A company produces two different versions of a certain product. Let q₁ indicate the amount produced of the first version. The cost function c(q₁) for the first version (expressed in euros) can be described by the equation c(q₁) = 9₁ · √√0.59² +59₁ 10 a) For which value(s) of q₁ is the instantaneous rate of change of the cost function equal to 1.75? You may use the graphical calculator to find zeros of a polynomial function if needed. b) Using the result from a), give a precise economic meaning for the instantaneous rate of change of 1.75. We now denote 92 as the amount produced of the second version. The equation of the cost function c(9₂) for the second version is unknown. We do know that the current cost for a production of 2 units of the second version is 50 monetary units and that the elasticity of the cost in terms of the produced amount when 92 = 2 is equal to 1.88. c) Give a linear approximation ƒ of the cost function c(9₂) for production amounts close to q₂ = 2.The function P(x) = -4.75x² + 1900x sold. Find a) the profit when 75 units are sold 3000 gives the profit when a units of a certain product are dollars b) the average profit per unit when 75 units are sold dollars per unit c) the rate that profit is changing when exactly 75 units are sold dollars per unit d) the rate that profit changes on average when the number of units sold rises from 75 to 150. dollars per unit e) The number of units sold when profit stops increasing and starts decreasing. (Round to the nearest whole number if necessary.) unitsThe revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even. R(x) = 200x – 2x2; C(x) = - x + 35x + 5000; 0sxs100 The manufacturer must produce units to break even.
- Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is МС- 4x+ 25, that its marginal revenue is MR%3D 75 - 6х, and that the cost of production of 60 units is $8,880. (a) Find the optimal level of production. units (b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level.Company XYZ projects their revenues for the given quarter to be modeled by the function R(z) = 12z - 6z + 2000, where x represents the number of goods sold and R(x) the price. The fixed costs for Company XYZ include rent and wages, and is a total of 10000 each month and the variable costs for the quarter can be modeled by the function V (2) = 12x + 1000. (a) Find the break-even point for Company XYZ. [ Select) (b) Find the marginal profit function. I Select ]x+2 (1) Find the rate of change of the function f(x) (ii) The number of units Q of a particular commodity that will be produced with K with respect to x when x = 1. 1- 8x thousand dollars of capital expenditure is modeled by Q(K) = 500 Kố. Suppose that capital expenditure varies with time in such a way that t months from now there will be K(t) thousand dollars of capital expenditure, where 2t* + 3t + 149 K(t) t+2 (a) What will be the capital expenditure 3 months from now? How many units will be produced at this time? (b) At what rate will production be changing with respect to time 5 months from now? Will production be increasing or decreasing at this time?
- The total cost a power plant ($/megawatts) to produce electricity is Y=12+1.3X+0.24 X2 , where X is in megawatts. The estimated selling price of electricity is (16-0.23X) per megawatts. Find the value of X that maximizes profit. Group of answer choices Less than 10 megawatts Between 10-12 megawatts Between 12-14 megawatts More than 14 megawatts Dont(c) Consider the aggregate production function Y = K = 100,000, A = 8, and N = 128. K0.2 (AN)0.8 Compute output whenThe revenue function R(x) and the cost function C(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even. R(x) = 200x - x; C(x) = 5x+ 7250; 0sxs 100 The manufacturer must produce units to break even.