4. Suppose the total revenue function is 4x2 + 3x + 2. Find the average and marginal revenue. In addition, find the values which maximizes TR. Suppose, however, that the total revenue. is y 4x³+3x2+2x, find the average, marginal, the value which maximizes y.
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- 5. Demand functions are X-100-Px and Y=152-2Py Total Cost is C-6x2 + 4y2 +4xy + 110, Optimize the profit using two variable regular optimization formula.nou Given cost and price (demand) functions C(g) = 110g + 43,000 and p(g) = - 1.8q + 890, what price maximizes revenue? len It would be $ per item. (Round answer to two decimal places.) llab lome Quiz Grade Study Goody11:30 l 4G I Homework 4 (section 2.1-2 & 2.2).pdf Economic Mathematics (1) Name ID Section 2.2 Revenue, cost and profit 1. If the demand function of a good is given by P-80 – 3Q, the fixed costs are 100 and variable cost are 5 per unit. Work out the profit when Q-10. 2. Find an expression for the profit function given the demand function 20+P= 25 and the 32 +5. Find the value of 0 for which the firm average cost function AC = (a) breaks even (b) makes a loss of 432 units (c) maximises profit. 2/2 !!
- Given cost and price (demand) functions C(q) = 100q + 41,000 and p(q) = - 2q + 890, what price maximizes revenue? My Co It would be $ per item. Cours (Round answer to two decimal places.) Anno Calen CullA 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 function(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?
- On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…
- PROBLEM No 1INTERPRET ALL THE RESULTS!!! Demand equation of a producer is: P = 270 * Q - 2,4 * Q² a) Which is the expression of the TOTAL REVENUE FUNCTION TR b) Which is the expression of the MARGINAL REVENUE MR c) For Q=25 calculate the value of TOTAL REVENUE FUNCTION d) Find the marginal revenue function MR for Q = 15 u. and explain the result found. e) Find the maximum revenue. Max TR(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡 三 = 9 ..3. Johnny Rockabilly has just finished recording his latest CD. His record company's marketing department determines that the demand for the CD is as follows: Price Number of CDs $24 10 000 22 20 000 20 20 30 000 18 40 000 16 50 000 14 60 000 The company can produce the CD with no fixed cost and a variable cost of $5 per CD. a. Find total revenue for quantity equal to 10 000, 20 000, and so on. What is the marginal revenue for each 10 000 increase in the quantity sold? b. What quantity of CDs would maximize profit? What would be the price? What would be the profit? c. If you were Johnny's agent, what recording fee would you advise Johnny to demand from the record company? Why?
