If the price charged for a candy bar is p(x) cents, then x X 10. p(x)=151- a. Find an expression for the total revenue from the sale b. Find the value of x that leads to maximum revenue. c. Find the maximum revenue. a. R(x) =
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- Maximizing Revenue The price p (in dollars) and the quantity x sold of a certain product obey the demand equation (a) Express the revenue R as a function of x. (b) What is the revenue if 15 units are sold? (c) What quantity x maximizes revenue? What is the maximum revenue? (d) What price should the company charge to maximize revenue? (e) What price should the company charge to earn at least $480 in revenue?The representative consumer of a soft drink has a weekly demand given by the function P = 1 – 0.075Q and the cost of producing the soft drink is C = 0.4Q (where Q is the number of cans of soft drink). Show that, instead of selling the product case by case, it is in the firm's interest to make the soft drink available in 8-can packages at a price equal to the cost of production plus consumer surplus. (hint: calculate the profit per consumer in both versions)The demand functions for a pineapple is given by p=-0.10x+15. a.) find the revenue function b.) how many pineapples will you sell when you are maximizing revenue? c.) what price gives the maximum revenue and what is the maximum revenue?
- All consumers have identical demand for a pint of pistachio ice cream. Each person has a demand function of P = 30 – 2Q, where P is the price and Q is the number of pints. Marginal cost is $2. Design a two-part tariff and calculate profits.Find the demand function for the marginal function below. Recall that if no items are sold, the revenue is $0. R'(x) = 0.03x2-0.08x + 196Suppose the average age of Stanford Alumni increased at the same time the smaller stadium was built and the income elasticity of ticket sales is .5 Group of answer choices Tickets are an inferior good. If income increases with age, it is more likely the smaller stadium will increase total revenue because any increase in ticket revenue from the increase in prices will be reinforced by an increase in ticket sales from the higher income of Stanford Alumni. If income increases with age, it is less likely the smaller stadium will increase total revenue because any increase in ticket revenue from the increase in prices will be offset by a decrease in ticket sales from the higher income of Stanford Alumni.
- The demand function of a good is P = (123 - 5Q)0.6 .Find the value of Q which maximizes total revenue. Round your answer to 1 decimal place.Suppose that the demand for a product is given by the following demand function: Q = 500 -3P A. To sell 200 units, what price should you charge?In a small college town there is only one movie theater. In a given month, if the theater is open, the owners have to pay a fixed amount of $6,000 for the films, ushers, etc., regardless of how many people come to the movies. For simplicity, assume that if the theater is closed, its costs are zero. The demand function for movie tickets in the town is characterized by ??= 45−QT/60 a. Find the profit-maximizing price and quantity of movie tickets, and indicate them on the graph above. How much would the theater make in profits? b. Suppose the local government implements a property tax, so that each month the theater now must pay a lump sum tax of $700. What will be the price and quantity of movie tickets under this tax?
- The manager of a bicycle shop has found that, at a price (in Rands) of p(x) = 150 –x/4 per bicycle, x bicycles will be sold . Answer the following:• Find an expression for the total revenue from the sale of x bicycles. (Hint: Revenue = Demand *Price. )• Find the expression for the quantity to be sold q if the demand function demand is given byp = -10q + 3200• What is the number of bicycles x, sold if the price is R40The demand function for football tickets for a typical game at a large midwestern university is D(p) = 200.000–10.000p. The university has a clever and avaricious athletic director who sets his ticket prices so as to maximize revenue. The university's football stadium holds 100.000 spectators. a)Write down the inverse demand function. b)Write expressions for total revenue and marginal revenue as a function of the number of tickets sold. c)Draw the inverse demand function and the marginal revenue function. On your graph, also draw a vertical line representing the capacity of the stadium. d)What price will generate the maximum revenue? What quantity will be sold at this price? e)At this quantity, what is marginal revenue? At this quantity, what is the price elasticity of demand? Will the stadium be full?Suppose the typical Buffalo Bills fan has the following demand curve for Bills football games:P= 120-10G where G is the number of games the fans attend.If the Bills want to sell the fan a ticket to all eight home games, what price must they charge?