The demand equation for a certain product is given by 'p = 112 - 0.04 x, where 'p' is the unit price (in dollars) of the product and 'x` is the number of units produced. The total revenue obtained by producing and selling 'x' units is given by R = x p`. Determine prices 'p' that would yield a revenue of 6850 dollars. Lowest such price dollars %3D Highest such price dollars
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- The demand function for device model ADN781 is given by p(x)=510−0.18x2, where pp is the unit price (in dollars) and xx is the quantity demanded (in thousands of units).If adverse conditions are driving the price up by $5 per week, find the rate at which the quantity demanded for device model ADN781 is changing when the price is $438.The monthly demand function for x units of a product sold by a monopoly is p = 5,700 − 1 2 x2 dollars, and its average cost is C = 3,020 + 2x dollars. Production is limited to 100 units.A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result only 40 units were sold in a week. The manufacturers fixed costs of production are $ 1710 a week and variable costs are $9 per unit. You are required to 4) Assuming a sudden change in trading conditions resulting in a 20% reduction in demand at all price levels, to find the equation of the new demand function and to recommend how the manufacturer should respond.
- Suppose a company has fixed costs of $41,600 and variable cost per unit of 2/5x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1776 − 3/5x dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x = 1300, 32---correct (b) Find the maximum revenue. (Round your answer to the nearest cent.)$ 1314240----- correct(c) Form the profit function P(x) from the cost and revenue functions. P(x) = ????? Find maximum profit.$ 401956--- correct(d) What price will maximize the profit? (Round your answer to the nearest cent.)$ ??? only need help on c and dSuppose a company has fixed costs of $46,800 and variable cost per unit of 2/5 x + 333 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 2159 − 3/5 x dollars per unit. Form the profit function P(x) from the cost and revenue functions. P(x) =The demand function for a certain product is determined by the fact that the product of the price and the quantity demanded equals 8000. The product currently sells for $3.50 per unit. Suppose manufacturing costs are increasing over time at a rate of 15% and the company plans to increase the price p at this rate as well. Find the rate of change of demand over time.
- Suppose a company has fixed costs of $57,600 and variable costs of 4 9 x + 222 dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is 2054 − 5 9 x dollars per unit. Find the maximum revenue.The cost per unit of producing a product is 280 + 0.2x dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $420, how many units should the firm produce and sell each week to maximize its profit? unitA company can manufacture at most 200 units per month. About x units per month can be sold at the price p(x) = (500 – x) dollars and the cost of producing x units per week is C(x) = 150 + 4x + x2 dollars. Find; a. Revenue from sale of x units per week b. Maximum weekly profit and the number of units produced to obtain the maximum d. Marginal Revenue at Maximum weekly profit level c. Marginal cost functions at Maximum weekly profit level
- A manufacturing process has a total cost function given by the equation C = 10 + 4x and a total revenue function given by the equation R = 22x - 4x2 where x is the quantity produced in ’00 units and C and R , are both N$’00. i. Using the cost equation, C = 10 + 4x, identify the value of the company’s fixedcosts (i.e. those that remain constant irrespective of the quantity produced) andvariable costs (i.e. those that vary according to production) for thismanufacturing process. ii. Construct a table to calculate the value of C and R using the values 0, 1, 2, 3, 4and 5 for x. iii. (Using the data from the table in (ii), plot a fully labelled graph for C and Ragainst x. Use the graph drawn in (iii) to determine:iv. The quantity of units produced where the manufacturing process breaks even(i.e. where neither a profit nor a loss is made). v. The range of x in which the manufacturing process makes a profit and the rangein which the manufacturing process makes a loss. vi. The profit or loss…Suppose that a company has determined that the demand equation for its product is 5x + 3p - 30 = 0 where p is the price of the product in dollars when x of the product are demanded (x is given in thousands). The supply equation is given by 52x - 30 p + 45 = 0, where x is the number of units that the company will make available in the marketplace at p dollars per unit. Find the equilibrium quantity and price.Suppose a company has fixed costs of $12,300 and variable cost per unit of $0.20 x+128 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 236 − 0.8x dollars per unit. Give the functions for Revenue, Cost, and Profit: R(x) = C(x) = P(x) =