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- 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 the demand function is p=100-4q, find the level of output at which total revenue is maximum and also find the maximum revenue.The price p (in dollars) and the quantity q sold of a certain product obey the demand equation q p = − 800 20 and 0 40 p (i) Express the revenue R as a function of q. (ii) What is the revenue if 20 units are sold? (iii) What quantity q maximizes revenue? What is the maximum revenue? (iv) What price should the company charge to maximize revenue? (v) What price should the company charge to earn at least $3500 in revenue? Please answer with step by step process
- The demand function for a particular brand of LCD TV is given by p = 1480 − 20x where p is the price per unit in dollars when x television sets are sold. (a) Find the revenue function. R(x) = (b) Determine the number of sets that must be sold in order to maximize the revenue.sets(c) What is the maximum revenue? $ (d) What is the price per unit when the revenue is maximized?$ per unitGiven the demand function. P=16?−0.02? • Determine the quantity and price at which total revenue will be maximized. • test the second-order condition.Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demand for these two cameras are as follows (DS = demand for the Sky Eagle, Ps is the selling price of the Sky Eagle, DH is the demand for the Horizon and PH is the selling price of the Horizon): Ds = 225 - 0.6 Ps + 0.3 PH DH = 270 + 0.1 Ps - 0.58 PH The store wishes to determine the selling price that maximizes revenue for these two products. Select the revenue function for these two models. Choose the correct answer below. (i) Ps Ds + PHDH = PH(270 - 0.1 Ps - 0.58 PH) + Ps(225 - 0.6 Ps + 0.3 PH) (ii) Ps Ds - PH DH = Ps(225 - 0.6 Ps + 0.3 PH) - PH(270 - 0.1 Ps - 0.58 PH) (iii) Ps Ds + PH DH = Ps(225 - 0.6 Ps + 0.3 PH) + PH(270 + 0.1 Ps - 0.58 PH) (iv) Ps Ds - PH DH = Ps(225 + 0.6 Ps + 0.3 PH) - PH(270 - 0.1 Ps - 0.58 PH) Find the prices that maximize revenue. Do not round intermediate calculations. If required, round your answers to two decimal places. Optimal Solution: Selling price of…
- Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demand for these two cameras are as follows (DS = demand for the Sky Eagle, Ps is the selling price of the Sky Eagle, DH is the demand for the Horizon and PH is the selling price of the Horizon): Ds = 230 - 0.5 Ps + 0.38 PH DH = 260 + 0.1 Ps - 0.62 PH The store wishes to determine the selling price that maximizes revenue for these two products. Select the revenue function for these two models. Choose the correct answer below. (i) Ps Ds + PHDH = PH(260 - 0.1 Ps - 0.62 PH) + Ps(230 - 0.5 Ps + 0.38 PH) (ii) Ps Ds - PH DH = Ps(230 - 0.5 Ps + 0.38 PH) - PH(260 - 0.1 Ps - 0.62 PH) (iii) Ps Ds + PH DH = Ps(230 - 0.5 Ps + 0.38 PH) + PH(260 + 0.1 Ps - 0.62 PH) (iv) Ps Ds - PH DH = Ps(230 + 0.5 Ps + 0.38 PH) - PH(260 - 0.1 Ps - 0.62 PH) Answer: Option 3 Find the prices that maximize revenue. Do not round intermediate calculations. If required, round your answers to two decimal places. Optimal Solution:…The average revenue function for a commodity is p = 50 – 4q. Find edp when: demand = 5 units ; price = Rs. 6. Find consumer’s surplus at price = Rs. 6A firm faces a demand function D(p), for which the revenue- maximizing price is $10. The demandfunction is altered to 2D(p). What is the new revenue maximizing 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.Reid has determined that the daily demand for doughnuts at his favorite bakery is described by the following equation: Qd = 3,300 - 3000P where Qd is the daily quantity demanded in number of doughnuts and P is the price per doughnuts in dollars. a. What is the point price elasticity of demand at a price of $0.70? b. Assume the price is currently $0.70. What is the marginal revenue obtained by selling one additional doughnut? c. The marginal cost of producing an additional doughnut is $0.10. What price should the bakery establish in order to maximize profits?Demand for Corn Flakes is: P = 17 - Q. Supply of Kellogg's Corn Flakes is: P = 2 + Q. Now a generic company enters the market, selling generic Corn Flakes for $5. Assume consumers are indifferent between generic and Kellogg's Corn Flakes. How many boxes of corn flakes will sell in total (both brand and generic)? Enter as a value.