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Consider the following price-
P = 80 − 4Q, {Q/0 ≤ Q ≤ 10}
(i) Sketch the price-demand function
(ii) Find the revenue function.
(iii) Suppose C = 20 + 5Q , find the profit function
(iv) Calculate the profit if Q=8
(v) Find the break-even level of output
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- Consider the following price-demand function: P = 80 − 4Q, {Q/0 ≤ Q ≤ 10} (i) Sketch the price-demand function(ii) Find the revenue function.(iii) Suppose C = 20 + 5Q , find the profit function(iv) Calculate the profit if Q=8(v) Find the break-even level of output You have to solve iv and vThe marketing research department for a company that manufacturers and sells gaming systems established the following price-demand function p(x)=240-30x Where p(x) is the wholesale price in dollars at which x thousand gaming systems can be sold, Find the revenue function when x thousand units are demanded Find the value of x that will produce maximum revenue. What is maximum revenue to the nearest thousand dollars? What is the price per gaming system that produces the maximum revenue?Suppose the demand equation is where x is the number of items sold when the per unit price is p dollars. Determine (a) the revenue function, (b) the domain revenue function, (c) the revenue derived from the sale of the 100th item-the marginal revenue when x = 100, (d) estimate the level of production that maximizes the revenue, and the maximum revenue.
- (i) If the demand function for a particular commodity is p=−0.09x+51 and the total cost function C(x)=1.32x2+11.7x+101.4,where x is the level of production. Find (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?A firm faces the following linear inverse demand for its product P = 60 - 2Q. a) Find the firm's total revenue function TR (Q). b) Find the expression for the firm's marginal revenue. c) Assuming that the marginal cost of production is given by MC=8. What will be the equilibrium output and price?Suppose the equilibrium price in the market is $10 and the price elasticity of demand for the linear demand function at the market equilibrium is -1.25. Then we know that: demand is inelastic. marginal revenue is $2. marginal revenue is $50. demand is unit elastic.
- The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)The demand function for a firm is; Qd = 122,000 - 500P + 4M +10,000PR where, Qd is quantity demanded, P is price per unit. M is income, and PR the price of a related good. The estimated the valueS of M and PR will be Rs 3200 and Rs 4, respectively. The firm's estimated average variable coSt function IS; AVC = 500 - 0.03Q + 0.000001Q2 a. Find the profit maximizing level of output of the firm and the price to charge. b. Should the manager continue production or shut down? Explain your answer. c. Find the level of output at which the average variable cost is at its minimum.Suppose the demand function for a product is given by the function: D ( q ) = − 0.02 q + 80 D ( q ) = - 0.02 q + 80 Use integration (or other appropriate methods) to find the following: (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4 , 000 q = 4 , 000 .) A) The total actual revenue for q = 3 , 350 q = 3 , 350 units: Answer 1: B) The total possible revenue (for all quantities and prices): Answer 2: C) The Consumer's surplus corresponding to q = 3 , 350 q = 3 , 350 units: Answer 3: D) The "Not Sold" value corresponding to q = 3 , 350 q = 3 , 350 units: Answer 4
- A toy manufacturing from has demand for the product is given by the demand function Q= 500 - 3p. Where P is the price in dollars and q is the quantity sold per year. To sell 200 units, what price should the firm charge.please solve question 4- Prove that total revenue is maximized for a linear demand function, P = a - bQ point where Q = a / 2 * b . - Minimize the following cost function: TC = 1/3 * Q ^ 3 - 8.5Q ^ 2 + 60Q + 27If demand function is given as the following: Qz = 230 -2.75 Pz + 0.5 I + 1.2 Pm + 0.6A Where Qz is quantity of Good z sold, Pz is price of Good z per unit, I is per capita income, Pm is price of competitor and A is the amount of advertising spent. Current values: Pz= RM 55 I= RM 9000 Pm= RM 50 A =RM 12,000 a) Should the firm consider giving a price discount in order to increase total revenue?