A firm's demand function is given by p 234 - 5q, where p and q denote the price and quantity, respectively. The firm has fixed costs of £165 and variable costs of £132 per unit produced. Find the firm's total cost function C(q), revenue function R(q) and profit function (q), and consider the following statements. Which of these statements is true? %3!
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- Suppose a product's revenue function is given by R(q)=−6q2+400q, where R(q)is in dollars and qis units sold. Also, it's cost function is given by C(q)=103q+3333, where C(q)is in dollars and qis units produced. Find a simplified expression for the item's Marginal Profit function ( MP(q)) and record your answer in the box. Be sure to use the correct variable. (Use the Preview button to check your syntax before submitting your final result). Answer: MP(q)=A commodity has a demand function modeled by p = 106 − 0.5x and a total cost function modeled by C = 30x + 33.75, where x is the number of units. (a) What unit price (in dollars) yields a maximum profit? $ per unit (b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) $ per unitThe 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)
- Answer b and c Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) a. Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. b. Now consider two cases: (i) Company is effectively able to price discriminate in thetwo markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit maximizing levels of price,output, and the total profits? c. Analyze,…Q1. A firm faces the following average revenue (demand) curve: P = 100 - 0.01Q where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 50Q + 30,000. Assuming the firm maximizes profits, a. What is the level of production?A price-taking firm's variable cost function is C = Q3, where Q is the output per week. It has an avoidable fixed cost of $1,024 per week. Its marginal cost is MC = 3Q2. What is the profit maximizing output if the price is P = $192? 0 or 5.33 or 8 5.33 or 8 0 or 5.33 0 or 8
- Suppose a company has fixed costs of $31,200 and variable cost per unit of 1 3 x + 444 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1768 − 2 3 x dollars per unit. Find the break-even points. (Enter your answers as a comma-separated list.) Find the maximum revenue. (Round your answer to the nearest cent.) Form the profit function P(x) from the cost and revenue functions. Find maximum profit. What price will maximize the profit? (Round your answer to the nearest cent.)Define Q to be the level of output produced and sold, and assume that the firm’s cost function is given by the relationship TC = 20 + 5Q + Q2 Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationship Q = 25 - P a. Define total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.) b. Determine the output level where total profits are maximized. c. Calculate total profits and selling price at the profit-maximizing output level. d. If fixed costs increase from $20 to $25 in the total cost relationship, determine the effects of such an increase on the profit-maximizing output level and total profits.Answer B,C,D A firm can produce at most x = 2500 units per month, and their marginal cost function has been computed to be MC=1200+x , while the cost of producing and selling 30 units is $70,000. If their marginal revenue function has been computed to be MR=3500 , then find: The number of units of production resulting in maximum monthly profit The maximum monthly profit Associated fixed costs How many units does the firm need to manufacture and sell in order to break even?
- Question Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Now consider two cases (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? c. Analyze, with graphs, the two alternative pricing strategies…– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units. Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price. Find the Revenue and Cost functions, both of which are dependent on price p. Write the Profit function. Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale. Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph. Algebraically find the price that results in a maximum profit. Conclusion: A price of $_________ results in a quantity of _____________ units…Wakanda is a firm that solely supplies vibranium to Marley and Paradis. The demand function of the Marley market is given as QM=110-PM , and the demand function of the Paradis market is QP=30-PP . Wakanda’s total cost in producing vibranium is given as TC=100+10Q , where represents a ton of vibranium. 5. Compute the mark up price on each market and interpret the results.