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) = 1.60 + 0.10x – 0.0012x. Also, the shop will lose $70 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. P(x) =
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- 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)=1.40 +0.02x -0.0006x². Also, the shop will lose $75 per day at a sales level of x = 0. Find the profit from operating the shop at a sales level of x ties per day. P(x)=given the function c(x) = 100 + 8x + 0.1x^2 find the marginal profit At x = 50 if the price per unit is 20A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?
- Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. Graph the profit function, M(x)=550x-3x²-8000, and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): number of sales:The cost function for Acme Laundry is C(q)=50+30q+q2, where q is tons of laundry cleaned. What q should the firm choose so as to maximize its profit if the market price is p?
- 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 HintThe market for high-quality matsutake mushrooms is dependent on the weather. If the weather is good, one kilogram matsutake mushroom can be sold for $30. In bad weather it sells for only $20 per kilogram. Matsutake mushrooms produced one week will not be kept until the next week, A small matsutake mushrooms producer has a cost function given by C = 0.5q^2 + 5q + 100 where q is weekly matsutake mushrooms production. Production decisions must be made before the weather (and the price of matsutake mushrooms) is known, but it is known that good weather and bad weather each occur with a probability of O.5. How much matsutake mushrooms should this firm produce if it wishes to maximize the expected value of its profits?Average and marginal profit Let C(x) represent the cost ofproducing x items and p(x) be the sale price per item if x items aresold. The profit P(x) of selling x items is P(x) = xp(x) - C(x)(revenue minus costs). The average profit per item when x items aresold is P(x)/x and the marginal profit is dP/dx. The marginal profitapproximates the profit obtained by selling one more item, given that x items have already been sold. Consider the following cost functions Cand price functions p.a. Find the profit function P.b. Find the average profit function and the marginal profit function.c. Find the average profit and the marginal profit if x = a units are sold.d. Interpret the meaning of the values obtained in part (c). C(x) = -0.02x2 + 50x + 100, p(x) = 100 - 0.1x, a = 500
- A toy manufacturer's cost for producing q units of a game is given by Ca) =1450 +3.69 + 0.0006g. If the demand for the game is given by p = 8.6 - 4409 how many games should be produced to maximize profit? (Round your answer to the nearest integer.). 888 X gamesFind the marginal profit. C(x)=4x^2; R(x)=x^3+5x+15A firm's profit is determined by subtracting the cost of production from its revenues. Suppose we have Binjin Company selling pins at a price of p = 45. Its cost function is C(y) = y³ – 9y2 + 60y + 10, y 2 0, for y units of pins sold. Define the Binjin Company's profit function T(y) and find the interval over which it is concave and the interval over which it is convex. Draw a rough sketch of the graph of a(y) (Hint: You will be able to sketch the graph by determining the values of T(y), T'(y), and t"(y) at critical values.).