Suppose we know that p=1,056- D/5, where p: price in dollars and D = annual demand. The total cost per year can be approximated by $1,000 + 2D². a. Determine the value of D that maximizes profit. b.Show that in part(a) profit has been maximized rather than minimized. c. Find the maximum profit
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- 1. ThedemandfunctionforagoodisgivenbytheequationP=a−bQwhilethetotalcost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit.(b) Derive an expression for the value of Q for which profit is maximised.6. Let p(x) = 4 – 0.0002x be the price (in TL) of each unit of a certain product required to attract a demand of x units in a year and let C(x) = 600 + 3x be the total cost of producing x units of the product in a year. (a) (- as large as possible? What is the number of units that should be produced to make the yearly profit (b) What is the yearly profit in case (a)A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 75 – 0.1D units (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,000 per month and the variable cost is $30 per unit produced. Solve, a. What is the maximum profit per month related to thisproduct? b. What is the range of profitable demand during a month?
- The total profit from the sale of q sweatshirts is: P(q) = 5q – 0.005q2 – 450. a. Calculate the additional profit earned when 450 sweatshirts are sold. ________ b. Calculate the additional profit earned when 750 sweatshirts are sold.A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p= 75 -0.10 (D is the demand or quantity sold per month and p is the price in doilars). The fbxed cost is $1.000 per month and the variable cost is $30 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month? a. The maximum profit per month for this product is S (Round to the nearest dollar.) b. The range of profitable demand during a month is from units to units. (Round up the lower limit and down the upper limit to the nearest whole number.)Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal revenue for a product is MR = 1800 and the marginal cost is MC = 90Vx + 4, with a fixed cost of $600. (a) Find the profit or loss from the production and sale of 5 units. There is a -Select-- | of $ (b) How many units will result in a maximum profit? units
- A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is p= 200-0.05D where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $15000 per month and the variable cost is $50 per unit. a. What is the number of units that should be produced and sold each month to maximize profit? b. What is the domain of profitable demand during a month? Show your spreadsheet.(b) The total revenue curve of a firm is R(q) = 40q – 12q² and its q- 12.85q + 20 + 30 400 where q is the firm's output. average cost A(q) Derive an expression C(q) for the firm's total cost function. Derive an expression II(q) for the firm's profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firm's profit is maximize v. What is the firms's maximum profit? i. ii.1. (a) A company expects fixed cost of $55,000. Margin is to be 46 percent of the retail. Variable cost in addition to costs of goods is estimated at $0.06 per dollars of sale. Find the profit function using s for sales volume. (b) Square Hospital Limited charges every COVID patient a fixed amount for using their ICU facilities. What would be the graphical nature of the demand function of ICU in this case ? (c) Write down the general form of the Augmented matrix of a system of Linear Equation which consists of 5 equations and 4 unknowns. (0.5 0.5 (d) Calculate the steady state vector for the given transition matrix: (e) Assuming the nonnegativity constraints for each variables, calculate the total number of corner points for the following system of inequalities: 2x + 5y + 4z 2 29 3r + 2y + z 2 23 10r + 8y +5z > 62
- show calculations A wheat seed dealer has a cost function: C = 100 + 20Q +Q2. Inverse demand is: P = 620 -2Q. Maximum profit is: A. 38,400 B. 36,200 C. 39,200 D. 29,900 Handwritten solution not required correct answer will get instant upvote.ect of the utility commission's ruling on the profitability of the firm? 15 A company estimates that the demand for its product fluctuates with the price it charges. The demand function is q = 280,000 – 400p where q equals the number of units demanded and p equals the price in dollars. The total cost of producing q units of the product is estimated by the function C = 350,000 + 300q + 0.0015q? (a) Determine how many units q should be produçed in order to maximize annual profit. (b) What price should be charged? (c) What is the annual profit expected to equal? 16 Solve the previous exercise, using the. A call center in India used by U.S. andU.K. credit card holders has a capacity of1,400,000 calls annually. The fixed cost ofthe center is $775,000 with an averagevariable cost of $2 and revenue of $3.50 percall.(a) Find the percentage of the capacitythat must be placed each year tobreak even.