不 A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x) dollars per tie, where MP(x) = 1.25+0.08x-0.0024x2. Also, the shop will lose $90 per day at a sales level of x=0. Find the profit from operating the shop at a sales level of x ties per day. -
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- A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?Suppose the firm achieves total revenue of $1,000 by selling 150 units while facing total costs of $900. If the firm produces and sells 151 units, its total revenue is $1,005, and its total costs are $950. Should the firm produce and sell the extra unit? Group of answer choices yes, since marginal profit is positive yes, since profits are positive no, since marginal profit is negative no, since marginal profit is positive You have recently learned that the company where you work is being sold for $1,000,000. The company's income statement indicates next year's profits of $30,000, which have yet to be paid out as dividends. Assuming the company will remain a "going concern" indefinitely and the interest rate will remain constant at 7%, at what (constant) rate does the owner believe that profits will grow? (Hint: the price the owner was willing to pay is the present value of the firm's future cash flows) Group of answer choices 6% 5% 4% 4.5%The market for smart thermostats has grown increasingly competitive. Producers of smart thermostats all rely on the same technology and face the same costs. The cost function for a smart thermostat producer is given by the following function: c(y)=-10y+2003 where y stands for the number of smart thermostats produced and sold in a month. 2nd attempt Suppose the market demand for smart thermostats in any month is given by QD = 305 - p. In the long-run equilibrium, we would expect to find firms in the industry. See Hint
- Given cost and price (demand) functions C(g)= 110q + 44,600 and p(g) = - 2g + 860, what is the marginal revenue at a production level of 55 items? The marginal revenue is $ . (Round answer to nearest dollar.) Pr rith11.2 The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 36x − 0.01x2. (a) Find the marginal cost function C'(x). C'(x) = Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears. $ per teddy bear Compare this with the exact cost of producing the 101st teddy bear (in $). The cost is increasing at a rate of $ per teddy bear. The exact cost of producing the 101st teddy bear is $ . Thus, there is a difference of $ . (b) Find the average cost function C, and evaluate C(100) (in $). C(x) = C(100) = $ per teddy bear What does the answer tell you? The average cost of producing the first hundred teddy bears is $ per teddy bear.If the demand function for math self-help videos is given by 45 -0.4x, and the total cost function to manufacture the videos is given by 4x + 17, evaluate the marginal profit function at x = 10. Marginal Profit = This means that if production and sales increase by one unit, then total profit will O increase decrease by approximately dollars.
- The company AffordableStuff sells cell phones. The marginal cost for each cell phone is given by the equation C(x) = 0.01x² – 3x + 229. a is the number of cell phones manufactured and sold. The marginal revenue function is R(x) = 429 – 2.x. Both C(x) and R(x) are given in dollars. a) Where do these curves intersect? What do those intersection points mean? b) Find the area between the curves, using end points that make sense. Round to the nearest cent. c) What does the area under the curve mean in this case?You sell items. Your marginal revenue and marginal cost are given by the formulas: MR (q)= 9.344-0.8q and MC (q)= 0.1q2-1.2q+5.9 where q is measured in hundreds of items and marginal revenue and marginal cost are in dollars per item. Compute the change in total cost that occurs if quantity increases from 225 to 226 items.***What would this look like in EXCEL, Graph and Table*** The cost function for Acme Laundry is: TC(q)=10+10q+q^2 so its marginal cost function is: MC(q)=10+2q where q is tons of laundry cleaned. Derive the firm's average cost and average variable cost curves. What q should the firm choose so as to maximize its profit if the market price is p? How much does it produce if the competitive market price is p = 50?
- A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³ -0.3x² +600x-800. Currently the company builds and sells 7 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 6 laptops weekly? c) What is the marginal profit when x = 7? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 8 laptops weekly a) The current weekly profit is $ (Round to the nearest cent as needed) b) The decrease in profit is $ (Round to the nearest cent as needed.) c) The marginal profit when x=7 is $ (Round to the nearest cent as needed) CLOT d) The profit resulting from the production and sale of 8 laptops weekly is approximately $ (Round to the nearest cent as needed)2.1 A manufacturer estimates that its variable cost for manufacturing a given product is given by the following expression: C(q) = 25q² + 2000q [$] where C is the total cost and q is the quantity produced a. Derive an expression for the marginal cost of production b. Derive expressions for the revenue and the profit when the widgets are sold at marginal cost.Should a firm shut down if its weekly revenue is $1,000, its variable cost is $500, and its fixed cost is$800, of which $600 is avoidable if it shuts down? Explain.