Use the functions given below to solve the problem. C(x) represents the cost, in dollars, of x units of a product and R(x) represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold even. order to break C(x) = 72,000 + 43x and R(x) = 47x The number of units that must be produced and sold in order to break even is units.
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- Pepper farming is carried out in a greenhouse. Proceeds from the sale of pepper, R,dollars per square meter is determined by the following function. R = 5T (1-e^-x) where T is the temperature set in the greenhouse (Celsius, C^0)and the amount of fertilizer per square meter (kilogram, kg) the costs are as follows: fertilizer cost per square meter is 20?, heating cost is 0.10^2.According to this information a) type the profit function of the manufacturer,?(?, ?).B) determine the end points of the profit function.c) show which endpoints you specify or which ones give the highest amount of fertilizer with the temperature value that makes the profit.The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=26x +18,625 and R(x)-200x-0.2x² for 0≤x≤ 1000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0sxs 1000. Find the break-even points. Find the x-intercepts of the graph of P(x) (A) R(x) has a horizontal tangent line at x =The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)
- Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).Assume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.Assume that it costs a company approximately C(x) = 400,000 + 160x + 0.002x2 dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- v than the average cost from (b). This means that the average cost is ---Select--- v at a production level of 10,000 smartphones. Need Help? Watch It
- A company has cost and revenue functions, in dollars, given by C(q) = 6000 + 10g and R(q) – 12q . (a) Find the cost and revenue if the company produces 500 units. Does the company make a profit? What about 5000 units? Enter the exact answers. The cost of producing 500 units is $ The revenue if the company produces 500 units is $ | Thus, the company a profit. The cost of producing 5000 units is $ The revenue if the company produces 5000 units is s Thus, the company a profit. (b) Find the break-even point. Enter the exact answer. The break-even point is |units. Which of the following illustrates the break-even point graphically? 50000 R(g) C(q) 40000 30000 20000 10000 1000 2000 3000 4000 5000 50000 40000 30000 - 20000 10000 R(g) C(g) 1000 2000 3000 4000 5000The estimated cost to produce x items is given by the function: C(x) = 0.004x² + 5x + 6000 Determine the average cost and marginal cost of producing 2,000 items and calculate the level of output for which the average cost is the lowest and what that cost is.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 MC = 2x + 25, that its marginal revenue is MR = 43 − 4x, and that the cost of production of 80 units is $8,560. (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. There is a ---Select--- profit loss of $ .
- 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 MC = 2x + 25, that its marginal revenue is MR = 73 – 6x, and that the cost of production of 80 units is $8,560. (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. There is a -Select--- v of $As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500, the cost for one capital is $250. If the production plan is to produce 100 products, what is the firm's minimized cost 5,000 8,750 10,000 7,500A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $25,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x). V(x) = 0.000001r' – 0.01r? + 50x The company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x). R(x) = -0.02.r² + 150r (0 < x < 7500) (a) Find the total cost function C. C(x) = %3D (b) Find the total profit function P. P(x) = (c) What is the profit for the company if 1,600 units are produced and sold each week?
