19) A beverage company works out a demand function for its sale of soda and finds it to be q-D(x)=3300-26x, where q- the quantity of sodas sold when the price per can, in cents, is x. At a price of 118 cents per can, will a small increase in price cause the total revenue to increase, decrease, or stay the same? A) Decrease B) Stay the same C) Increase 19)
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- A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functiondemand for a product is related to its selling price P (in dollars) by the equation n=2800-100p where n is the number of fans that can be sold per month at a price P. Find the selling price that will maximize the revenue.A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result only 40 units were sold in a week. The manufacturers fixed costs of production are $ 1710 a week and variable costs are $9 per unit. You are required to a) Show the equation of the demand function linking price (P) to quantity demanded (X) assuming it to be a straight line is P = 118-x
- . Revenue The revenue from the sale of a product isgiven by the function R = 400x - x3. Selling howmany units will give positive revenue?Consider the demand function d(p)=300e^−0.01p^2 items purchased when charging p dollars per item. Currently the price is 9 dollars per item. Use marginal analysis to estimate the decrease in demand when the price increases by 0.3 dollars per item. Demand would decrease by approximately _____ items. Round your answer to three decimal places.2. Suppose your marketing research department estimates the demand for your company’s product as Qx= 500-11Px+0.5Y, where Qx is the quantity demanded per week, Px is the price of product X, and Y is the average household income per week in the city. R2=0.87, the standard error of the coefficients of the price (Px) and household weekly income (Y) are 2 and 0.1, respectively. a. Are the coefficients of Px and Y statistically significant? b. Given the initial values Px=$10 and Y=$1000, find price elasticity (Ep) and income elasticity(EY), respectively. Is the demand for the company’s product price and income elastic, or inelastic? c. What action should the manager take to increase the company’s operating revenue? d. Is the company’s product a normal good? How do you know? e. Interpret what R2=0.87 means
- The weekly demand function for a particular product is q=f(p)=2400-15p. Where q is stated in units and p is stated in dollars. Determine the quadratic total revenue function, where R is the function of p. What is the concavity of the function? What is q intercept? What does total revenue equal at a price of 60 dollars.suppose that supply function of given by Qs=15+2P,and due tk market situation,the maximum price is 8 birr,then find the domain and range of the function?The demand function for a crrtain product is giving by p=500+1000/(Q+1). where p is tje price and q is the number of units demand. Fimd the average price as demand ranges from 49 to 99
- The price p (in dollars) and the quantity q sold of a certain product obey the demandequationq − 800 - 20P and 0 < p < 40 (answer iv and v) (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?Suppose the demand function for a product is given by pq+p=5000 where p is price in dollars and q is the number of units sold. If the price is $50 and increasing by $2 per week, how is the quantity sold changing?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 unit