If the total manufacturing cost 'y' of making x units of a toy is :' 25x-9000 y= 2 i) What is the variable cost per unit? ii) What is the fixed cost? (iii) What is the average cost of manufacturing 5,000 units?
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- The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?How are the absolute maximum and minimum similar to and different from the local extrema?A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 2.4 times as much as the concrete (per unit of surface area). If the volume of the silo is 550 m^3, what are the dimensions of the silo (radius and height of the cylindrical tower) that minimize the cost of the materials? Assume the silo has no floor and no flat ceiling under the dome. What is the function of the cost of the silo C, in terms of the radius r. C = (type an expression. Type an exact answer, using pi as needed)
- A total cost function (in dollars) is given by C(x)=194+9x+0.68x2 .Use differentials to estimate the change in cost when the level of production is changed from 86 to 88 units. Step 1 of 2 : Find the number of units sold that will yield maximum revenue. Round your answer to the nearest whole unit.The company is conducting set of experiments to maximize the time needed to discharge the battery. It was found that the time (t) is proportional to different powers of acceleration (a) , mass (m), and energy (E) of the battery. Use dimensional homogeneity to find the formula of the time and the value of overall dimensionless proportional constant using t=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 1D km/hr, and the mass is 14D-pound.Find the number of units x that produces the minimum average cost per unit C in the given equation. C = 0.001x3 + 3x + 250 x= units
- 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 dA 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…A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the dome costs 1.6 times as much as the concrete (per unit of surface area). If the volume of the silo is 500m^3,what are the dimensions of the silo (radius and height of the cylindrical tower) that minimize the cost of the materials? Assume the silo has no floor and no flat ceiling under the dome. What is the function of the cost of the silo, C, in terms of the radius, r?
- 14. The quantity, Q, of a certain product manufactured depends on the quantity of labor, L, and of capital, K, used according to the function Q=900L1/2K2/3. Labor costs $100 per unit and capital costs $200 per unit. What combination of labor and capital should be used to produce 36,000 units of the goods at minimum cost? What is that minimum cost?A driver has to pay an annual road tax of $150. His car does 50 kilometers to one gallon which costs 50 cents per gallon. The car is serviced every 5000 kilometers at a cost of $40, and depreciation is calculated in cents by multiplying the square of the mileage by 0.01. (I) If he covers x kilometers in a year, compute an expression for the total cost in traveling x kilometers and the average total cost per kilometer. (ii) Show that the annual mileage which will minimize the average total cost per kilometer is around 1049 miles.Suppose a company has fixed costs of $54,400 and variable cost per unit of 4/9x + 222 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1856 − 5/9x dollars per unit. (a) Find the break-even points (b) Find the maximum revenue. (c) Form the profit function P(x) from the cost and revenue functions.